Considering this, can you use a radio as a guitar amp?
Yes. Your electric guitar requires an instrument cable, but you can get a converter type of adapter (maybe from Radio Shack or a music store) that will allow you to plug into the Mic In port. There may be some level difference, but not much it at all.
Beside this, can you use an old radio as an amp? If you are just playing at home or want one for recording you can now have your very own real tube amp for very little money. Use an old Tube radio! Every Tube radio produced in the past consists of 2 major parts a receiving circuit and an amplification circuit.