Well that certainly didn't take very long. The folks over at XDA, as they like to do, have unlocked the Verizon Galaxy Note 2 bootloader. You'll need to jump through a few hoops and have some patience to get through it all, but if you're willing to do it there's a pretty granular walkthrough at the source link below. Before you do, remember to hack at your own risk -- bad things can happen when you start messing around with this stuff.
Unlocking the bootloader still won't get rid of that big 'ol Verizon logo on the home button, though. You'll need a sticker for that job.