I rather liked the idea of lava spewing out of the hole, but I’m just going to take the question on merit and assume you really could drill a hole through the earth and jumped inside.
Would you pop up the other side? (Assuming, of course, the other side wasn’t under the ocean! Ooops.)
No. First, wind resistance would slow you down and you’d not get anywhere near the other side.
Second, you’d hit the side of the hole and die not long after jumping in because of the rotation of Earth.