A battery is only used to start the car. Once started everything is powered by the Alternator. Should the alternator go out you will run off your battery until it goes dead.
If you plan on driving it home with just battery power, do not turn on your radio, A/C or anything that requires power.
If you decide to purchase the car, I would just put down a small deposit; purchase an Alternator and then take it out for a ride to check it out.