It's a Courtyard in the middle of downtown Oakland. It's nowhere near the airport. It would take you at least thirty minutes to travel to the airport. The parking isn't part of the hotel. It's near the hotel, but it's in what is likely a privately owned garage, rather than part of the hotel.

Even if it were an open, free parking lot in the middle of nowhere, walking distance from the airport, owned by the hotel, the answer would still likely be no.

But, as with anything, stranger things have happened. Call and ask the hotel. Even if they give you the likely "no" answer, you are no worse off than if you didn't call.