saeco: i think that a resign means you lose a backgammon as long as you haven't moved out any piece

You mean moved a piece off the board? No, it's a backgammon only if there are pieces in the opponent's home or on the bar and none of your own already borne off.

iirc, you can't resign and lose a gammon

If you resign when you're clear of your opponent's home then you'll be asked to confirm losing a gammon.