Most likely not. I will pretty much pick up any board between 160-164cm.
Unless the 162cm was already on the largest/smallest part of your range, I doubt that going 3 cm in either direction will matter much.
Rome is supposed to be generally good, although stay away from the United's (at least this year's model. they got recalled so if you see some out there stay away).
From what I heard, Ride has good bindings (some of the older models have problems with screws, but I think they fixed that). Also, they make them out of metal rather than plastic (which I like, given my previous experience with a United...).
K2 has a pretty good variety of bindings as well. Formula's are going through a big overhaul for next year. Haven't really heard anything bad about any of the models. Probably would skip the Indy and Sonic models, though
Technine sucks from what I've heard.
Burton: I'm not familiar with their EST system. Might stay away from Burton as their bindings are meant to go with that system at the moment?