By making people join those sites to win a contest, you're essentially telling those folks that they're not invited to the party.
So you're not invited.
I'm not sure why so many organizations today think they have to measure the success of their outfit by how many FB "likes" they get, particularly when they are overtly asking people to bump up their count, which to me sort of defeats whatever integrity that is supposed to have.
It's the modern day equivalent of "Sign up for this mailing list for a chance to get a free prize." Nothing more.