Almost 100% yes. There are some carts that can't take cards, so you can't charge to the room with those, and there might be non-disney-owned stores that wont' do it, but for the most part yes, you just show them your keycard for the disneyland resort hotel, and it goes straight to the room. Very convenient.
In addition to the above room charge conditions you can also have purchases sent back to your Disney Hotel. That way you do not have to carry them around all day. Usually pick them up the next morning at bell desk.