Gravity isn't a force, strictly speaking. Objects move along geodesics in spacetime (that's basically a straight line along a curved surface), and gravity bends spacetime, and therefore also these geodesics, around massive objects. So you don't actually get accelerated by gravity, that's why you don't feel anything during free fall. What we perceive as the force of gravity pushing us down, is the solid ground accelerating us upwards, when following the geodesic would have us fall instead.

So when the sun disappears, the geodesic that used to spiral around the sun suddenly straightens out, and the neutral movement, the new free fall, has the earth continuing in a straight line. You wouldn't be able to feel that. What the other person said about tidal forces is true tho, it would likely cause worldwide tsunamis