What happens if someone who is not elect tries to seek God?

Although I had abandoned answering any questions here due to the difficulty of posting my answers, I am compelled to give you my perspective.

Since this is a Christian answer site I can only assume that you are asking about seeking the God of the Bible, and I will answer it in that context (from the Bible). As far as any other Religion is concerned that must be asked on a different site.

Exactly what you mean when you say elect I cannot know, but as far as I can determine from the Bible God's elect refers to those whom he has chosen. With this in mind let's see what we can learn from Scriptures.

All Scripture is quoted from the King James Translation.

In the Old Testament (King James Translation), The term elect is used only in the Book of Isaiah:

Isaiah 42:1 Behold my servant, whom I uphold; mine elect, in whom my soul delighteth; I have put my spirit upon him: he shall bring forth judgment to the Gentiles.

Isaiah 45:4 For Jacob my servant's sake, and Israel mine elect, I have even called thee by thy name: I have surnamed thee, though thou hast not known me.

Isaiah 65:9 And I will bring forth a seed out of Jacob, and out of Judah an inheritor of my mountains: and mine elect shall inherit it, and my servants shall dwell there.

Isaiah 65:22 They shall not build, and another inhabit; they shall not plant, and another eat: for as the days of a tree are the days of my people, and mine elect shall long enjoy the work of their hands.

In the new Testament Jesus used the word elect seven times:

Matthew 24:22 And except those days should be shortened, there should no flesh be saved: but for the elect's sake those days shall be shortened.

Matthew 24:24 For there shall arise false Christs, and false prophets, and shall shew great signs and wonders; insomuch that, if it were possible, they shall deceive the very elect.

Matthew 24:31 And he shall send his angels with a great sound of a trumpet, and they shall gather together his elect from the four winds, from one end of heaven to the other.

Mark 13:20 And except that the Lord had shortened those days, no flesh should be saved: but for the elect's sake, whom he hath chosen, he hath shortened the days.

Mark 13:22 For false Christs and false prophets shall rise, and shall shew signs and wonders, to seduce, if it were possible, even the elect.

Mark 13:27 And then shall he send his angels, and shall gather together his elect from the four winds, from the uttermost part of the earth to the uttermost part of heaven.

Luke 18:7 And shall not God avenge his own elect, which cry day and night unto him, though he bear long with them?

And in the remainder of the New Testament it is used nine times:

Romans 8:33 Who shall lay any thing to the charge of God's elect? It is God that justifieth.

Colossians 3:12 Put on therefore, as the elect of God, holy and beloved, bowels of mercies, kindness, humbleness of mind, meekness, longsuffering;

1st Timothy 5:21 I charge thee before God, and the Lord Jesus Christ, and the elect angels, that thou observe these things without preferring one before another, doing nothing by partiality.

2nd Timothy 2:10 Therefore I endure all things for the elect's sakes, that they may also obtain the salvation which is in Christ Jesus with eternal glory.

Titus 1:1 Paul, a servant of God, and an apostle of Jesus Christ, according to the faith of God's elect, and the acknowledging of the truth which is after godliness;

1st Peter 1:2 Elect according to the foreknowledge of God the Father, through sanctification of the Spirit, unto obedience and sprinkling of the blood of Jesus Christ: Grace unto you, and peace, be multiplied.

1st Peter 2:6 Wherefore also it is contained in the scripture, Behold, I lay in Sion a chief corner stone, elect, precious: and he that believeth on him shall not be confounded.

2nd John 1:1 The elder unto the elect lady and her children, whom I love in the truth; and not I only, but also all they that have known the truth;

2nd John 1:13 The children of thy elect sister greet thee. Amen.

In each of these instances the word elect refers to the chosen of God. In the Old testament, however; its usage does not appear to be as restricted as it does in the New Testament.

That having been explained now let's take a look at whose prayers God hears.

2nd Chronicles 7:14 If my people, which are called by my name, shall humble themselves, and pray, and seek my face, and turn from their wicked ways; then will I hear from heaven, and will forgive their sin, and will heal their land.

Here God says he will hear the prayers of Christians, on the condition that they conduct themselves in the proper Christian manner.

Psalms 10:17 Lord, thou hast heard the desire of the humble: thou wilt prepare their heart, thou wilt cause thine ear to hear:

Matthew 7:7-8 Ask, and it shall be given you; seek, and ye shall find; knock, and it shall be opened unto you: For every one that asketh receiveth; and he that seeketh findeth; and to him that knocketh it shall be opened.

Here we see that being humble is and asking is key to prayer.

So what prayers does God not hear?

Isaiah 1:11 through 15
To what purpose is the multitude of your sacrifices unto me? saith the LORD: I am full of the burnt offerings of rams, and the fat of fed beasts; and I delight not in the blood of bullocks, or of lambs, or of he goats. 12 When ye come to appear before me, who hath required this at your hand, to tread my courts? 13 Bring no more vain oblations; incense is an abomination unto me; the new moons and sabbaths, the calling of assemblies, I cannot away with; it is iniquity, even the solemn meeting. 14 Your new moons and your appointed feasts my soul hateth: they are a trouble unto me; I am weary to bear them. 15 And when ye spread forth your hands, I will hide mine eyes from you: yea, when ye make many prayers, I will not hear: your hands are full of blood.

If we can learn anything from this passage in Isaiah it is that God is only interested in hearing heartfelt prayers.

So finally let's see what we can find about God's reaction to those who seek him.

Deuteronomy 4:29 But if from thence thou shalt seek the LORD thy God, thou shalt find him, if thou seek him with all thy heart and with all thy soul.

The key here to finding God is in the sincerity of seeking him.

1st Chronicles 28:9 And thou, Solomon my son, know thou the God of thy father, and serve him with a perfect heart and with a willing mind: for the LORD searcheth all hearts, and understandeth all the imaginations of the thoughts: if thou seek him, he will be found of thee; but if thou forsake him, he will cast thee off for ever.

So the answer to your question appears to be that whether or not one is of the elect or not; God's reaction of either rejecting or accepting our seeking him is dependent on our sincerity in seeking him.

Hope this helps

The tough part of answering this question is understanding your meaning of "seek God." Of course the Reformed perspective on salvation (soteriology - study of salvation) is that no one with true faith can fall away. For a solid understand of this, read the Westminster Confession of Faith (WCF) chapters 14-18 (they are short); this is a fine place to read it, click here, where you can easily click on scripture proofs to the Reformed statements. The phrase "seek God" is used by Paul in Acts 17:27, but with carefulness, as seen by the surrounding words, "might" and "perhaps". Still, in the parable of the sower, Mark 4:3-20, Jesus speaks of some that have an apparent interest in the things of God, but then fall away. The key is outward interest vs. inward faith, as seen in I John 2:19. Look at the example of Felix, Acts 24:22-27, who showed some interest, and Agrippa, Acts 26:28, but never a sincere faith. So, from a Reformed perspective, no one with true faith ever falls away, but one may "[taste] the word of God, and the powers of the world to come" Hebrews 6:5, and lack a sincere relationship with God (a redeemed relationship, that is).

For more, read The Almost Christian Discovered; or, The False Professor Tried and Cast. by Matthew Mead, here or here

While I'm taking a risk by quoting just one verse--and only a portion of a verse at that--to support my contention, I'll venture forth, going where angels fear to tread:

"There is none that seeketh after God" (Romans 3:11b).

Whether my following statement does or does not reflect a Reformed, Calvinist perspective, I do not know, but here goes: Dead men and women do not seek after God. We all, by nature and by practice, are spiritually dead in trespasses and sins (Ephesians 2:1).

In other words, a spiritually dead person cannot seek after God. Period. Now an unregenerate person can be aware of God's "invisible attributes, His eternal power and divine nature" (Romans 1:20), but to seek after God, no. God therefore has to initiate the search. If He does not do it, it does not get done!

Does God ever not initiate a desire within an unregenerate man or woman, boy or girl? That is truly the sixty-thousand-dollar question! Frankly, I do not have a definite answer, one way or the other.

While it is true that only God knows those who are his (2 Timothy 2:19), is it also true that he initiates the desire within a human heart only if he knows in advance he or she is going to be "his"? Again, I do not have a clear and unambiguous answer for you.

Where does that leave us? Frankly, I think the answer is tucked away in the verse I've just quoted in part. In its entirety it reads,

"Nevertheless, the firm foundation of God stands, having this seal, 'The Lord knows those who are His,' and, 'Everyone who names the name of the Lord is to abstain from wickedness."

What is the connection between v.19a and 19b? Simply this: Never, on this side of eternity, can a regenerate person know of a certainty whether someone is going to be saved or not. It is simply not possible. Yes, we can conclude tentatively that a person is not currently regenerated because they lack spiritual fruit, but we can never say emphatically he or she is not one of the elect. Again, only God knows. I cannot stress this point too much.

Moreover, the Scripture attempts, I believe, to steer us away from trying to find out what only God knows; namely, who will seek after God and who will not. At the same time, however, Scripture says in effect, "Focus, rather, on your own life. Are you abstaining from wickedness? Are you bearing spiritual fruit which is worthy of one of the elect, one of God's true children?" That, my friend, is where the rubber meets the road, and not in trying to second guess God.

So we're back to where we started; namely, attempting to find an answer to your question of whether or not God "rejects" a person he knows is not one of his elect. Since only God knows those who are his, should not our priority as Christ followers to do everything in our power to take the truths of the gospel to every living creature? If and when we do so, God's Holy Spirit in some mysterious way takes God's word, as heard through our lips and seen through the quality of our lives, and initiates in a human heart the process of seeking after God.

[...] does the mere act of seeking God mean that the person must be elect?

Yes.

Reformed theology must be understood wholesale. If you pick and choose some ideas and don't put them in the context of all the other ideas it stops making much sense. This has to do with the presuppositions involved.

From a Reformed perspective the answer to this question is really easy. If anyone seeks God, they are the elect. They will find him because it isn't dependent on them in the first place (this is where irresistible grace comes in). It is only those that God has first called that will seek him, and those he calls he will save (meaning they are elect).

Romans 8:29-30 (ESV)
For those whom he foreknew he also predestined to be conformed to the image of his Son, in order that he might be the firstborn among many brothers. And those whom he predestined he also called, and those whom he called he also justified, and those whom he justified he also glorified.

Reformed theology finds no place in that continuum for half-way measures. Of course in this life all we ever see is snapshots somewhere short of "glorified", but those who seek God will find him because they only sought God in the first place because they had been called (and justified).

Of course you might have lots of people that say they seek God and don't find him, but if they do not find him this is only proof that the thing they were seeking was not God but a counterfeit. Many are those who think they are following God who actually are not. What they wanted and followed was a God of their own imagination, not the one true God. They will be surprised to learn that they never knew God.

Isaiah 48:8a (ESV)
You have never heard, you have never known, from of old your ear has not been opened.