Do Protestant catechisms teach that man is created by and for God, and God always draws man to himself?

The Heidelberg Catechism teaches that man in his natural state hates God, which is contrary to the idea that we are naturally drawn towards God in any way.

Q & A 4

Q. What does God's law require of us?

A. Christ teaches us this in summary in Matthew 22:37-40: "'You shall love the Lord your God with all your heart, and with all your soul, and with all your mind.' This is the greatest and first commandment. "And a second is like it: 'You shall love your neighbor as yourself.' "On these two commandments hang all the law and the prophets." 1 Deut. 6:5 2 Lev. 19:18

Q & A 5

Q. Can you live up to all this perfectly?

A. No. I have a natural tendency to hate God and my neighbor. 1 Rom. 3:9-20, 23; 1 John 1:8, 10 2 Gen. 6:5; Jer. 17:9; Rom. 7:23-24; 8:7; Eph. 2:1-3; Titus 3:3

The Westminster Larger Catechism also teaches directly contrary to the idea that man in his natural state is in any way attracted to the true God.

Q. 23. Into what estate did the fall bring mankind?

A. The fall brought mankind into an estate of sin and misery.

Q. 24. What is sin?

A. Sin is any want of conformity unto, or transgression of, any law of God, given as a rule to the reasonable creature.

Q. 25. Wherein consisteth the sinfulness of that estate whereinto man fell?

A. The sinfulness of that estate whereinto man fell, consisteth in the guilt of Adam's first sin, the want of that righteousness wherein he was created, and the corruption of his nature, whereby he is utterly indisposed, disabled, and made opposite unto all that is spiritually good, and wholly inclined to all evil, and that continually; which is commonly called original sin, and from which do proceed all actual transgressions.

The Baptist Confession of Faith of 1689 also teaches directly against this.

Paragraph 4. From this original corruption, whereby we are utterly indisposed, disabled, and made opposite to all good, and wholly inclined to all evil, do proceed all actual transgressions.

Rom. 8:7; Col. 1:21 12 James 1:14,15; Matt. 15:19

From a Lutheran perspective, we believe that people will have a "god," because we are naturally driven to look for something/someone for all good things (this is essentially Luther's definition of what a god is). So, we would agree with the statement in the Catholic Catechism that "man is a religious being." We also would cite St. Paul in Romans 1:19-20, Acts 14:15-17, Acts 17:22ff.

However, to know the true God, we need His revelation to us which comes through the proclamation of the Gospel of Jesus Christ, as well as through the Sacraments (Baptism and the Lord's Supper). It is through these means of grace that God calls us to Himself and justifies us sinners before Him on account of Christ. We are naturally turned away from the true God and need Him to bring us to Himself through these means.

The Small and Large Catechisms of the Lutheran Church talk about these in more detail, particularly in the Large Catechism's exposition on the First Commandment and in the exposition on the Third Article of the Apostles' Creed.

I'll quote from the statement about the Third Article, because the catechism makes the point that it is the Holy Spirit who brings us to faith in Christ for our salvation:

Just as the Son obtains dominion, whereby He wins us, through His birth, death, resurrection, etc., so also the Holy Ghost effects our sanctification by the following parts, namely, by the communion of saints or the Christian Church, the forgiveness of sins, the resurrection of the body, and the life everlasting; that is, He first leads us into His holy congregation, and places us in the bosom of the Church, whereby He preaches to us and brings us to Christ.

For neither you nor I could ever know anything of Christ, or believe on Him, and obtain Him for our Lord, unless it were offered to us and granted to our hearts by the Holy Ghost through the preaching of the Gospel. The work is done and accomplished; for Christ has acquired and gained the treasure for us by His suffering, death, resurrection, etc. But if the work remained concealed so that no one knew of it, then it would be in vain and lost. That this treasure, therefore, might not lie buried, but be appropriated and enjoyed, God has caused the Word to go forth and be proclaimed, in which He gives the Holy Ghost to bring this treasure home and appropriate it to us.