It could also leak out, loose heat, and drilling down to it could trigger earthquakes and eruptions.

The argument "it's big, we can't affect it" has been proven wrong in the case of the atmosphere, and again in the case of the ocean. It is no longer a sound argument.

"It's big, we can't drill more than a negligible fraction of the way to it" remains as true as ever. So, no, we cannot make it leak out, lose heat, or trigger earthquakes or eruptions. It will still be almost as hot in a half-billion years when the sun engulfs and vaporizes it, whatever we do.

Eruptions in Siberia, and later in India, not long ago geologically, released more heat in a (geologically) short time than we could use up in a million years, with no effect on the Earth's magnetic field.

Just because we haven't discovered giant planet-eating space aliens yet doesn't mean they don't exist.