Does a hammer toe hurt?

Maybe: If the deformity is severe enough it can hurt, or if the toe rubs on the shoe it will cause pain.

If it becomes: Arthritic and/or if a corn develops.

They may or may not: Not all hammertoes will hurt. Pain usually will result from the use of ill fitting shoes.

It can.: People can get hammertoes several different ways, including just an unlucky roll of the genetic dice, but the fundamental result is usually the same: a toe that has drawn back and no longer sits straight or "flat", and sometimes this can be very painful, whether due to the underlying arthritis or a callus that forms due to the deformity.