Subject: Falling "through" the earth

If you drilled a hole parallel but at least a 1,000 miles away from the center axis of the earth, and two people at either opening fall into this hole, would they pass each other and fall out each other's opposite end? I read MAY97's answer, but that concerned through the center. In my question you are never near the earth's center. This question assumes no air resistance or friction against the walls.

Re: Falling "through" the earth