If there's signatures he will believe it, no doubt. But I think he's going to have some coming to terms conflicts with his identity. Jon is a brooding, emo sort of man (probably gets that from Rhaegar
). He grew up believing himself a bastard with nothing to inherit and went to the Wall, when he was really a Prince/future King all along and potentially not a bastard? I think it would take some time for that to sink in. I think Jon would also wonder if Benjen knew/suspected it and if he had something to do with R&L escaping and why he chose to take the black, especially since Brandon died. Also, I think Benjen told Jon in both AGoT and season 1 that Jon should wait a couple of years before joining the Watch and that he didn't know what he'd be giving up, that he had never had a woman before, etc.