Yes, it will be crowded. Thanksgiving weekend is a very busy of the year at all of the parks, and SeaWorld is no exception.
Unbearable is a matter your family's definition, of course. Just like at Disney, I would try to eat lunch during the "off hours" (not between noon and 1:30 pm), or you could spend a ridiculous amount of time standing in line for food. And the shows will actually fill up, so you can't walk up at the last moment and expect to seat a party of 16 together at the Shamu show.
The upside of going at that time of year is that park hours are extended, and I suspect that they will have the Mystify fireworks show and Sea Lions Tonight running again during the evening hours.