I figured that, since using the same RNG seed means you get the same random numbers, battles wouldn't desync if you did that. At least, that's how I understand it would work. The lottery mini-game works on the same principle (setting a seed depending on the day so the lucky number is always the same in a given day).
It would be more secure to have the battle worked out by a host, but I don't think there'd be any risk in skimping on that in favour of convenience (faster, less information to transmit, etc.). I can't think of anything else that would cause desync.