Does bad esn means that the phone will not function?

Yes. You should probably get it fixed

A cell phone with a "bad ESN" is a phone which cannot be activated on the carrier it was manufactured for due to various reasons. This can be due to the fact that the original owner was dissatisfied with their current carrier and switched carriers, or had a billing dispute with their carrier and canceled service without paying the early termination fee, or they got behind on their bill. The ESN can also be bad due to the cell phone being reported lost or stolen.