Obviously, an MC who cheats on his girl comes off very differently than an MC who has the opportunity but chooses to remain faithful. But how does that translate into a game where we can just reload a save and do both? I think this hinges on whether we see the MC as a character in his own right, or as a (mostly) blank slate that the player controls.
If we see the MC as a mostly complete, mature character that the player exerts a small influence over, then the option to cheat will be a genuine hit to his "teddybear" appearance. Even if the player turns down the offer, the fact is that he might have. That forces us to mentally adjust our image of the MC to account for that. In effect, it means that that the MC has always been the sort of man who would cheat on his girlfriend given the right circumstance... which might not be very strenuous, depending on how you write it!
On the other hand, if we view the MC as an empty shell to be filled by the player (at least to the limits of a video game), then the option to cheat is merely indicative of the type of MC we are playing in a given runthrough. In this case, the option to cheat can instead enhance the MC's teddybear quotient, because it's up to the player to decide just how tempted the MC was by the offer. If we want to play a white knight type, we can keep him on the straight and narrow as clear proof of just how devoted he is to his girl. If we want to play a cad, we can enjoy the way he strings along his latest conquest. But either way, our thoughts are limited to the current 'version' of the MC.
I obviously can't speak to how you (Drifty) perceive the MC, but for myself I'd say the MC is closer to the pre-defined character than he is to a tabula rasa. We already have a long backstory for his relationship with Chris, Linda and Stephanie - not just the facts, but insight into what they meant to him, too. We've had numerous comments about the sort of man he is, from just about all the girls, without much input from us players. Even when asked why, for example, the MC saved Cece, we don't get the option to say he thought she was hot, or lie about his motives to keep up appearances. No, the answer is uniformly given for us: he saved a girl he barely knew on pure instinct. Heck, even the fact that the MC HAS a face in the first place contributes to the notion that he's the same core character no matter what choices we make.
So I guess that was just a really long-winded way of saying that I suspect you are right and giving us the option to make the MC cheat on his girl will ultimately change the way he's perceived (obviously the full impact would depend on the specific details). But I don't think that's an inherent result of the option, just of the way you have structured the story and the characters up to this point.