You probably could. I personally wouldn't attempt it because I mostly do software and wouldn't want to risk draining it dry overnight or voiding the warranty or something, but if it's a just a car battery it shouldn't be hard for someone with more EE knowledge.

Another option might just be to mount an entirely sperate power system just for the phone and any other devices. Buy a huge USB power bank off Amazon and mount it to the carriage or something, might not even need duct tape.