I'd agree with Spartan on this. Tony Stark wouldn't be as enraged as he was in that moment.
What is more interesting thusly is how this would affect the UN Sokovia Accords to police these metahumans since that did pass apparently.
Also Baron Zemo's intended manipulations wouldn't work in getting the Avengers to fight each other, so it would leave one to wonder what other avenue he would pursue to gain his vengeance since he seemed fairly capable, smart and competent enough to do what he did do. But if in his confrontation Steve Rogers had already disclosed the information to Tony Stark, then Zemo would've been captured (or killed himself) right off the bat.
But if Zemo knew that disclosure ahead of time, he would've had to try a different angle. But I'm not sure how he would know either way. Then again, hinging your entire plan on a literal assumption would seem uncharacteristic for him. So I'd imagine he'd make a plan for revenge across a different avenue.