Been rallying for some time, about 20 years, and no, I have never screeched any tires on a gravel road. An example, with standard engine in a old and slow very standard Volvo 940:
YouTube - Dackefejden ss1 Daniel Brorson
No road notes so that was why it was a bit slow in some parts, but did you hear any screech?
If you drive more slow in bends(without attack) or locks brakes before a bend, as first driver in a race (before any gravels comes loose) on salted road then there is a possibility but it would be unskilled dangerous driving.
I normally have about twice as strong engine as in the movie above, which makes it a bit simpler to drive with more attack before the bends, resulting in more gravel sound but I have never heard any screech.
I think you have Hollywood tires on your car.:grin: