No, there are separate buttons around the wheels.

As a different owner, pressing the accelerator while in FSD does not disengage. Keeping it pressed shows a warning that the car will not brake while you are overriding it. Holding it for a longer period (maybe 20s?) will start some warning feedback that will result in FSD disengaging after several more seconds. It also disengages if you exceed a set limit, which I think is 85, but I don’t hit that situation often.

Different models and years behave differently. Cars with no stalks use the right wheel.