If we dig a hole from north pole to south pole then jump into it from north pole will we come out?

Not a chance, many things would prevent this from ever happening.

A. We don't have technology good enough to dig that far into the earth.
B. Getting that close to the center of the earth would burn you alive
C. The center of the earth is where gravity comes from, so even if you got past the center gravity would start working in the opposite direction and pull you back in.
D. Falling for so long would more than likely get you enough speed that it would rip the skin off of your body, especially since you are getting closer and closer to the center of gravity, so you are going faster and faster.

However, if you managed to somehow ignore these problems then in all technicality, yes. You would appear on the other side of the world at the south pole, seeing as how they are directly opposite each other.