If it fits perfectly. Unfortunately, the breaking probably deforms the two ends.

There's a process in optics called "optical contacting" where you take two super-flat surfaces, push them together, and they stick. This is used in some specialized components where there can be no gap or optical adhesive at the interface. The pieces really do stick together. With optics, you don't have to worry about the materials oxidizing at the surface.

Also if you break a rod in space, you'd better be holding on to both pieces. ;-)