From what I've seen of Alvin's character so far from the 80s and current cartoon, I could see him cheating on his girlfriend or wife. To me anyways, he seems like the type of guy that would have multiple girlfriends. I honestly have trouble liking his character, since he's a selfish jerk and he's very sexist as shown in the episode "Soccer to Me".
Before getting to the question, let's address the other points in the post. As we've seen Alvin has traditionally had many love interests and can at times easily bounce from one girl to the next. His selfishness is part of the reason I'm not a huge Alvin fan though most of the time he doesn't intend to hurt anyone and they are multiple times in which he actually does good to others (or times when he realizes he was wrong, he still can't always admit it). I would say the level of sexism Alvin has isn't too over the top (boys tend to think they are better than girls or doubt their abilities at some things, and of course it can be reversed too).
That being said, based on what I've seen, I don't really think Alvin would cheat on someone he's in a serious relationship with, much less Brittany. It's been shown multiple times that he cares for her, and, despite the ease he can sometimes fall for other girls (or flirt with them), I believe he wouldn't go quite that far. "Stand By Your Man" may have been an instance of cheating, but it's not specific.