I mean, what can he do? Give the MC another black eye and bring him into a fight again? Honestly I don't think anyone else would really care, a fuck's still a fuck, and Tommy ain't anyone special. If he gets his panties in a twist it's his problem. Don't like it, Tommy? I'll see you in the parking lot, bro.
I don't believe her whole relationship with Chad was a lie. I think it was halfway in that Chad thought 'Ah shit, I'm gay now, but I gotta stay with Sage because she's hot and people would know I'm gay if I broke up with her and the alphas might trash me because of it'. They had no obligation to hook up at the beginning, so why if not for mutual attraction?
The idea of 'doing the right thing' is subjective. That's why phrases such as 'a white lie' exist. While lying or keeping secrets isn't exactly the proper thing to do, sometimes they're done to protect a person. Sage is trying to move on from Chad, and just telling her about this might rekindle her obsessive fire with their past relationship. And even if you tell her about it, what good would that do? That doesn't change the fact that Chad seemed to have cheated on her.
If anything, if you really want to tell her about it, I'd prefer if the MC just goes ahead and confronts Chad about the whole situation. We all know that Sage is slightly unstable, and given her current situation, she could lash out at Chad before he even gets the chance to explain himself. Chad doesn't seem to be that hostile towards the MC (I'm not sure if this changes depending on whether you defended him in front of Burke or not), and they might be able to sit down and have a civil conversation.
And if you did tell Sage about it, what would she do? As you've seen, she doesn't seem to be a fan of direct confrontation, and instead seems to have the habit of implying things in her speech. She could even beat herself up for not noticing that he was gay earlier, or say that she noticed the signs but thought that it was just in her head. With all her bottled up emotions, there's no telling what could happen. Hell, she might even just walk over to Chad's and beat his ass after learning some martial arts from MC.
When the choice arises, to tell or not to tell about Chad's secret, my first choice would be to keep it under the blanket. I'll still replay the game and go for the other choice, but that'd be my first choice. Or, it could be that the whole campus finds out entirely somehow and the MC doesn't even need to do anything.