Theoretically, yes. Ila, we have to ignore friction, the rotation of the earth and other complications. If we treat the mass distribution in the earth as uniform, a person could fall into the tunnel and then return to the surface on the other side in a manner much like the motion of a pendulum.
Assume that the person's journey began with an initial speed of zero kilometers an hour. His speed would increase and reach a maximum at the center of the earth, then decrease until he reached the surface-at which point the speed would again fall to zero.
Kwahiyo, one will oscillate repeatedly through the tunnel. I think ;-)