Not to speak for wedrifid, but I agree with their main point, and I would not predict this.

What I would predict is that fewer people in such a group would dodge the question (and those that did would dodge it less strenuously) than in a group where everyone projected disapproval of throwing people under trolleys.

I would further predict that the reduction in dodging (DR) would be proportional to how confident the subject was that the group really did disapprove more of dodging the question than of throwing people under trolleys... that is, that the group wasn't lying, and that he wasn't misinterpreting the group norm. Given that priors strongly suggest the opposite -- that is, given that most groups are more opposed to throwing people under trolleys than avoiding a question -- I would expect obtaining significant confidence to be nontrivial.

Relatedly, I predict that DR would be proportional to how certain the subject was that their answer would be kept confidential.

By the way, as long as we're doing this exercise, I'd also predict that people who don't dodge the question in normal settings, but rather claim they'd throw someone under the train, are more likely to be contrarian in general -- that is, I'd expect that to correlate well with making other controversial claims. This is even more true for people who often bring up trolley problems in ordinary conversation.