Yes it does happen… I have worked as a private relationship expert and life coach to the rich and famous for many years, I know everything YOU need to know about this subject.
What the married man does about falling in love with a woman who is not his wife will depend very much on his personality and the situation he is in. It will also depend on why he was cheating on his wife and seeing another woman in the first place. You can take 500 married men who fall in love with another woman and you will have 500 different outcomes and thoughts, so we have to generalise..
If a married man is constantly being unfaithful to his wife or looking to then he is just a player and probably should not be married. It makes you wonder marriage: is there any point? When the man is a player who should really be single and does not love his wife or value monogamy then it would be pointless for him to leave his wife for the other woman. For one thing he has no idea of how and is too immature and lazy to make any relationship work as a committed serious long term thing. He may very well believe he is in love with this new woman but she is a passing fancy just the same as his wife was at one stage. He may think he loves her simply because he finds her exciting or enjoys the sex, but that does not mean he is actually in love with her. If he leaves his wife to be with the other woman, which is very unlikely, then the same pattern will probably repeat itself, with him becoming bored with the new relationship just as he did with his marriage, and then he would be looking to cheat on this new person. It is possible but very unlikely that it is true love or that he can remain interested in and faithful to this new woman. If you are seeing such a married man then you are better off to enjoy it while it lasts and see it as a fun only short term thing or to walk away.
Every married man comes to a point where he asks himself should he divorce his partner.
When the man is truly unhappily married and was maybe tricked into marriage or forced into it somehow, and has a lot of genuine love to give to the woman he is seeing then things are different. The problem with such married men is that they often get torn between love and obligations or love and familiarity and even if they long to leave their wife they rarely feel they are able to or can bring themselves to. These men are fine to date if you like living alone and are independent and have a busy happy life in other ways, and do not expect anything such as marriage or living together with this man. Presumably because he genuinely loves you and cares for you he will make sure he spends a lot of time with you, otherwise I would not bother. It may hurt but it may well be better to walk away and be alone or find someone more available then.