No, the black hole at the center of the Earth, if one were to exist (which is purely speculative and not supported by current scientific understanding), would not be usable for faster-than-light space travel.
Black holes are regions of spacetime with extremely strong gravitational forces, where the escape velocity exceeds the speed of light. In the case of a hypothetical black hole at the center of the Earth, its gravitational pull would be immense, and any object or spacecraft falling into it would be unable to escape its gravitational grip.
While black holes are intriguing objects in astrophysics, they do not provide a means for faster-than-light travel. According to our current understanding of physics, the theory of relativity prohibits objects with mass from reaching or exceeding the speed of light.
The study of black holes has contributed significantly to our understanding of gravity, spacetime, and the universe. However, utilizing black holes for space travel, especially in a way that bypasses the speed of light limitation, remains purely speculative and beyond our current technological capabilities and scientific understanding.