I would say center of gravity moves a little, not much but i am sure it affects a little, why would riders otherwise move backwards, sideways and up and down on the bike to make it behave different in different situations? I at least used my body a lot when riding all the time trying to ride around the small problems that gets cured with setup, because you can't cure it 100% with setup, another problem will most of the time come
Just my thoughts on this, not a physics expert lol