Anything that crosses the event horizon of a black hole cannot escape the pull since it has crossed the Schwarzschild radius and thus, the escape velocity is greater than the speed of light, and since "nothing can travel faster than the speed of light", well the body is stuck there. But, if tachyons travel faster than the speed of light, then they must be able to escape from the pull of the black hole beyond the Schwarzschild radius.

But does their imaginary mass somehow interfere with the equations of General Relativity making them unable to escape the gravitational pull of the black hole?