That's a great question & I do not know the answer to it. We do not use the hotel for cruise parking, just the stay. They always ask if we're leaving our vehicle and we choose not to.
Call the hotel, they're super friendly and will give you the best information directly.
We stay at the hotel, then the morning of the cruise we head over to the Sunflower Bakery & Café for breakfast. After stuffing our faces, we drive to Galveston Park N Cruise, drop off the car & walk to the port.