Maybe. In a more controlled situation things could (and likely would have) gone better. However it also could have clouded his judgement when it came to investigating Bucky's innocence. The reason I think it would have is because Tony at the end of Civil War already knows Bucky is an innocent man before he snaps, and he snaps anyway and doesn't care. So knowing Bucky killed his parents before hand could made Tony knowingly ignorant of the truth even further in advance. And, even pre-Civil War, Tony has had moments where he's gone a bit unhinged and had moments of emotional instability. Stark in Iron Man 2 is borderline suicidal for a good chunk of the movie and in the first Avengers movie he loses his shit because Cap called him out for being a dick.
Yeah, that's perfectly true. Tony does not have the mental stability that Steve has. He just doesn't. He got PTSD from the Chitauri invasion, while Steve was just fine. Tony is constantly questioning himself on whether he's doing the right thing, while Steve is relatively more confident about his morality. This isn't to say Tony is weak or shouldn't be a hero, but he's just more vulnerable than him. Nevertheless, as the ending of Civil War shows, Tony can get back up so long as he has actual time and care to cope.
I also think there is a rivalry that plays into his psychology. Tony mentions how he percieves, with jealousy, how flawless Steve appears to be. Tony sees Steve as an impossible measure that he can't live up to no matter how hard he tries. His father constantly talked about the Great Captain America, while he clearly had a less favorable opinion of Tony himself. Now that he's known Cap personally for years, he sees that all the stories were true.
Keeping this in mind sheds yet another layer on the conflict he and Steve have. Tony desperately wants to be in the right and have Steve be in the wrong, just this once.
Just this once, Tony wants to have the moral high ground where he is doing the right thing, while Steve is doing wrong by being blinded by his feelings toward his friend. You can almost read his thoughts on his expression when he gets the files showing that Steve was right about the Winter Soldiers in the airplaine. "Goddammit. Of course, he's right again. " and you can sense his disappointment in himself at being the fuck up yet again.
So, head hung low, he goes to the Hydra base to help Cap and his friend with the Winter Soldier problem, like he should have done from the beginning.
Edit: I went back and Gif'd it. His frustration at finding out that he was, yet again, wrong is very palpable.
