The acceleration compensators - which are written up in just about every CT adventure or supplement that details starships - states that they cancel all movement affects and that crew and passengers get no sense of acceleration at all.
And what about missiles impacting the ship? Do the compensators compensate for that, too, along with the relative motion of the ship - which may be under the influence of Manuever/Evade and jinking madly, or do the players have to throw themselves around the room to simulate it?
I would think that impacts would at least cause something to happen inside the ship.