From my understanding of the story of Sodom and Gomorrah, God agrees to spare the cities even if a few righteous people live there. In the Christian age, our righteousness is imputed to us by Christ's atoning sacrifice. Does this mean that God's judgement will not come to pass as long as there a Christians living in a region?
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.
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.