I think it is believable because we are transported into the world being described. It was a time of decadence and self-indulgence. Although people still self-indulge today, it was more socially acceptable then.
Yes, I would say what happens is believable for the time period in which this novel is set and still is believable today. Tom Buchanan is a wealthy, bored man who cheats on his wife. He has an attractive wife and small daughter, yet he is looking for different thrills from a different class of people. This is a common theme in both life and literature; the wealthy man is attracted by something different, a woman who looks up to him and his money. In real life, look at the tragedy of Anna Nicole Smith. Myrtle Wilson is bought by Tom Buchanan and all his position and wealth seems to offer. This is the common motif of entrapment in a material, shallow world where money can purchase sex but not love.