BUT - that is what car chargers are for re: cell phones.

Sorry, Becca, but Nope. A Cell phone being charged has nothing to do with it - if the tower is down, so the cell phone can't communicate with it (by radio waves) you still have no service.

A "cordless" phone is something else entirely & requires mains power for the handseet to communicate to the base (also by radio waves)- unless its one where the base has backup batteries (some do, or at least used to" "cordless" phones plug into a land-line phone jack.