No. Best thing he could've done was telling Sage right after he found out that Jade was her mother or at least, as soon as possible. It's Sage we are talking about here...
The thing Sage hates the most are lies. The reason she was so pissed off with Chad was not just because he cheated on her, but also because he didn't own that fact when she confronted him, he tried to lie and gaslight her instead.
If the MC went and told her the truth, she would smack him and punch him and yell at him and would calm down afterwards and rationilize that it wasn't the MC that was doing something wrong, it was her mother.
Jade was the one that was married and not him, Jade was the one that went after a guy the age of her own kids and not him, Jade was the one that was fucking her own student and not him... Sage is one of the most understanding characters in the game, she would never blame him. She would actually like his honesty.
But Tremolo is the most mentally challenged character in the game because he should know who Sage is after getting to know her. And dude he had the audacity to say that Chad lacked balls to be honest with Sage... dumbass.