Sodom and Gomorrah and God's judgement in the Christian age

No. Believers are protected through whatever tribulation. Noah and his family through the flood, Lot, his wife, and daughters from the destruction of Sodom, and the city of Nineveh from destruction.

Acts 1;11 Which also said, ye men of Galilee, why stand ye gazing up into heaven? this same Jesus, which is taken up from you into heaven, shall so come in like manner as ye have seen him go up into heaven.

Jesus Christ is coming back just as he promised.

Matthew 24;3,4,5,1,

3 Tell us, when shall these things be? and what shall be the sign of thy coming and of the end of the world? 4 And Jesus answered and said unto them, Take heed that no one deceive you. 5 For many shall come in my name, saying, I am Christ; and shall deceive many. 14 And this gospel of the kingdom shall preached in all the world for a witness unto all nations; and then shall the end come.

God's plan is already set, believers are to watch, pray and be ready,

Matthew 24;13 But he that shall endure unto the end, the same shall be saved.

A class of Christians who believe in a Pretrib Rapture that occurs before a 7-year tribulation period of God's wrath believe that God's judgment will not be unleashed upon the world until He takes all Christians out. So for that class of believer's perspective, it's true.

And drawing nigh he said: Wilt thou destroy the just with the wicked?

Genesis 18:2

And,

if this is so, then the Lord knows how to rescue the godly from trials and to hold the unrighteous for punishment on the day of judgment

2 Peter 2:9

The first passage is a reference to Abraham before Sodom, interceding with the Lord. The second is also speaking of Lot and Sodom.

In one sense, you could say that God is holding off judgment because of those who are and will be righteous because of Christ. This pattern is seen may times in Scripture.

There are some valid considerations, however.

In Sodom, the judgment was total, from which Lot was saved. Not all judgment is of the same degree. Certainly, God preserves His elect. But, no matter what it looks like, God is still just and faithful. One cannot judge adequately in this life what calamities God should and should not save people from, or what calamities are acceptable, or even who His elect even are (without personal insight, that is).

While the general truth is valid, even if God were to destroy the whole Earth with fire today, was He unjust? His righteous are with Him, whoever they are, and the wicked are consumed.

So, yes, as a general rule, but specific situations can be a little but tricky (e.g., whether God should or should not judge America similarly, which is how it is often raised).

Does this mean that God's judgement will not come to pass as long as there a Christians living in a region?

It seems as if there are two types of Judgment that God has.

Final

Revelation 20:12 And I saw the dead, small and great, stand before God; and the books were opened: and another book was opened, which is the book of life: and the dead were judged out of those things which were written in the books, according to their works.

Interventional

Romans 1:28 And even as they did not like to retain God in their knowledge, God gave them over to a reprobate mind, to do those things which are not convenient;

Another example of intervention is one that shows the accumulation of iniquity up to a limit that brings judgment.

Genesis 15:16 But in the fourth generation they shall come hither again: for the iniquity of the Amorites is not yet full.

It may be that iniquity in the present age has not reached the upper limit. It may be that the tribulation described in Revelation chapters six through nineteen will be a judgment brought on the whole earth. However, even during this time there will be Christians because they will be hunted down and executed.

Revelation 13:7 And it was given unto him to make war with the saints, and to overcome them: and power was given him over all kindreds, and tongues, and nations.

There is a present limit on evil.

2 Thessalonians 2:7 For the mystery of iniquity doth already work: only he who now letteth will let, until he be taken out of the way.

I do not see God's judgment impeded by the presence of Christians especially at the individual level. However, I do see an accumulation of global iniquity judgment that will come.