You can do either one. In order to charge on your KTTW card, you have to give them a credit card when you check in and have charging privileges put on your card. The front desk can print out a list of charges for you anytime, and I think you can view them on the television in your room as well.
We always do this, because we don't like to carry cash around, and it's so easy to just put everything on the room key. You can do this almost everywhere--even most of the snack carts take them now. I was looking over one of our old statements last night, and we had a ton of ~$3 charges for ice cream, popcorn, drinks, etc.
We also don't like to end up with 100 separate charges on our credit card. If you charge to your room, you'll get a printout of all your charges, and one big charge will go through on your credit card.