We have done online check in but of course the room won't be ready until later in the day. Will we get free parking at the theme parks that first morning even though we haven't physically checked in?
If you have to pay, get a receipt and let the front desk take care of the charge.
You could always just park at your resort and take the bus/boat/skyliner to the park.
I agree with Sandi - have them scan your MB, or if you don't have a MB, show them the reservation in MDE. If you end up having to pay, save the receipt - the front desk will refund your account.