Can apple tell if iphone has been jailbroken if the phone is dead?

My iPhone 5's charging port is not working, and the phone will not charge. Before the phone died, everything was working fine, except the charging port. The iphone is jailbroken, but if i take it into the apple store to be fixed, can they still see that the iphone has been jailbroken? The main question i'm trying to ask is: Can apple fix my iphone?

Added (1). The phone is completely dead, and can't be turned on until they fix the charging port.

Yes, I think they can