They'll know anyway - they've got hunting license records, 4473's (you know, the ones that Janet Reno didn't want to destroy), and the state equivalent of 4473's.
I've got mixed feelings on this one. As I indicated above, I think they already know who owns guns (though they may not know exactly how many or which ones somebody owns), and I think that open records would show that a lot of the anti-gunners pack as well. On the other hand, as a general principle I favor more privacy to less (pesky libertarian impulses!).