Would you feel any acceleration if you were in a spaceship accelerated by a gravity-assist? As surprising as it sounds, the answer is no, because there's no relative acceleration between you and the spaceship. If the spaceship fired its rockets, that would accelerate the spaceship and not you; therefore you would be "pushed" by the spaceship and would feel an acceleration. But if both you and the spaceship are experiencing the same gravitational forces, then apart from some small tidal effects, there would be no feeling of acceleration.