Not so much. It's more analogous to surfing on a wave. Any object with mass warps spacetime towards itself. This doesn't cause an infinite buildup of 'spacetim

Not so much. It's more analogous to surfing on a wave. Any object with mass warps spacetime towards itself. This doesn't cause an infinite buildup of 'spacetime' on the object's surface. There are concerns with built up energy in front of the spaceship but not being sent back to your origin.