First, no object could be accelerated to that speed. Relativistic effects make that impossible. However, gravity waves move at the speed of light so there is some delay in gravitational effects. I'm not a physicist, but I'm pretty sure that if your sun-sized object shot through the solar system at 99.9999% the speed of light, and passed between the Earth and the Sun, it would take about 4 minutes for the object's gravity to be felt by either the Earth or the Sun.