You'd probably lose all sense of direction once you get to the center, anyway. Not like you can use a compass. Although I suppose you could use laser guidance from the surface to point you in the direction to dig, or something.

I would imagine that if indeed you could dig as far in as the center of Earth, then you'd be okay, because obviously gravity wasn't strong enough to pull the dirt in from the sides of the hole you'd dug (which would, of course, bury you alive).