[Oshkalaboomboom]

You would achieve enough momentum to carry you past the point of zero gravity (the center), so that you would "fall upward" for a ways. Then you would lose the momentum and fall back, with slightly less energy until you passed the center going the other way, then you would oscillate back and forth before eventually coming to a stop at the equilibrium point -- the center.

I've heard this answer before, also referencing the Chinaman's point of view which was seeing somebody falling UP out of a hole.

[jjotto]

I might regret asking, but...

Isn’t it likely that at some point the center of gravity relative to your location would pull you into the wall of the tube?

[IronJack]

But you wouldn’t fall out of the hole on the other side. In fact, you wouldn’t make it to the opposite surface

You can’t gain more energy than you started with.