Think of air pressure as being the weight of the column of air above you, up into space. Air pressure, and viscosity, would continually INCREASE as you got closer to the center of the earth, so terminal velocity would decrease. You’d hit Vt while still near the surface, then slow down as you descended into an increasingly-thick soup. By the time you got to the center, you’d have very little kinetic energy left and wouldn’t go very far the other way.
With no air or any other energy-loss mechanisms, you’d make it all the way to the opposite end before your energy ran out, then fall back the other way in an endless oscillation. But before long, you’d wish you had some air.