You would think so , but not so much. Just like having a paid for airline ticket does not guarantee you a seat (yep it true) a car reservation even prepaid does not guarantee you a car will be waiting.
So far there have been plenty of cars when we have gone, but this is a very busy time. I would think that arriving early would give you a better chance as people are constantly returning cars. Late arrivals will be more difficult if there are low inventories.