First of all, unlike what the previous poster said, when you do online checkin now, you either have to verify your card already on file or add in a new one for charging privileges to your room.
To answer your question, no. They do not charge your card. They place a $1 hold on your card to verify that it is a valid card. This is from experience when I checked in last week. Oddly enough, (I had 2 separate reservations) the reservation that I needed to change the card on, the placed the $1 hold. On the reservation that I left the card on file, the $1 hold was not placed on it.