NG: Oh sure, I wouldn't rule that out - it might have even been the whole point of manipulating his birth in the first place. That said, Sisko's visions in Far Beyond and Rapture could just simply due to the fact that he was chosen by the prophets as their liaison to Bajor in the first place - no genetic manipulation needed.
But let's say because of his parentage, that he was biologically 'vision-ready', then why the need to be shot with the big energy blast in Rapture? In my opinion, that is what opened his mind up to the visions. Although despite "Bashir's" efforts to shut it down biologically - the prophets managed to send other visions to him anyway, starting with Far Beyond a year later. Maybe his brain did have super-resistant synapses, triggered by the blast - who knows?!?
Also of note, Kai Winn received visions from the pagh-wraiths, but I don't believe her genetics were manipulated at birth, nor was she part-wraith. Perhaps none of it matters. When crazy non-corporeal beings want to communicate with you, they just do.