The uppermost parts of the pipe (up past GEO) would; that's why it doesn't fall down. However, unless your pipe is strong enough, it'll rip in two, and the part

The uppermost parts of the pipe (up past GEO) would; that's why it doesn't fall down. However, unless your pipe is strong enough, it'll rip in two, and the part above GEO would fly away and the part below will fall down.