It may depend on which hotel and what city you are in. I have tried to use points unsuccessfully in Chicago, Indianapolis, Dallas and Oklahoma City. That is not to say that if you tried to talk to the hotel manager and offered to pay the up charge for the "park and fly" addition, that perhaps they would do it. It may also depend on how long you want to leave your car there and if it is a hotel close to the airport and therefore parking spots are a premium. Once I was allowed to leave my car without the extra charge when I was gone for only 3 days, but I was using the hotel on either end of my trip away. I would be very interested in what Joshm comes up with.
In Park and Fly rates in general - here's a new twist to keep an eye out for - below (Rate Rules) comes from the Crystal City Marriott (Arlington, Va.) at Reagan National Airport. Note the new language stating AFTER stay (I take this to mean that on top of the rate differential, in this case $40, you must first pay to park for your stay - $24 at this property). Perhaps not a deal killer (depends on how many nights you're gone) and certainly not yet written into every Park and Fly (not at Dulles Marriott....yet), but once again, we should never get into the habit of getting comfortable with Marriott.com rates; they are carving at every corner. Good luck toward a good outcome.
Experiences: Park Here, Fly There, includes 7 nights parking after stay, 1 day park here and fly there, roundtrip airport transportation, see Rate Rules
I think it varies by property. Some airport hotels require you to book a park-n-fly rate in order to get free parking. Last year I discoverd that the Courtyard located at Richmond, VA Airport will give all customers who spend one night up to two weeks free parking even if they pay with points. Since the hotel is a category 2 hotel this is a steal when using points since it will cover your parking expense in addition to hotel expense. The best thing to do is call the hotel ahead of time and see what their policy is.