They haven't said one way or the other, but I really hope not. I'd be incredibly surprised if they let you, honestly. Then again, I'm incredibly surprised that they shipped the game like this at all. I really wish they'd have segregated online characters from offline characters like they did with D2.
I'm secretly hoping that the PS4 version actually syncs with B.net and brings PS4 and PC players together in the same game. I have no reason to believe that will be the case, aside from the incredibly negative reputation that D3's endgame on PS360 is about to have in a few weeks/months. The rampant duping and save file editing really ruins the feeling of accomplishment you get for making it out of a tough situation or getting an epic piece of loot.