What happens if Aenys Blackfyre is granted safe passage and presents his claim to the Great Council of 233 AC?

Hard to say. Blackfyre strength was certainly on the wane after the Third Rebellion, but on the other hand the pickings were pretty slim at the Great Council. I suppose the major question is how attractive a candidate Aenys would have been, both in his person and his policies. For example, could he have promised and delivered on an end to the Blackfyre Rebellions?

Probably not. Given that Daemon III, as the son of Haegon, would have considered his uncle a usurper and had the Golden Company to back it up, I don’t think Aenys could have delivered on peace.