no, it won't be VZW branded should it be released here for other carriers.
it is my belief that Google will eventually sell the device on their site unlocked where you can buy it at full retail price ($649) for all 3, maybe even 4, major carriers. it's going to be a good while before this happens, though. by the time it does happen, quadcore phones will be either out or about to come out.
edit: i wouldn't doubt that you will also be able to buy it subsidized from Google/Best Buy or elsewhere.
Galaxy Nexus i9250 unlocked and rooted