If the cars alternator is not working or not hooked up then the car will run until the battery dies.
The alternator on a car doesn't just charge the battery it also keeps the battery charged and then takes over and provides electricity to the engines electrical components such as the spark plugs, ignition coils, fuel injectors etc.
If the battery is fully charged then you might be able to drive 10 to 20 miles until the battery goes dead on you.
If the battery is good but the alternator is bad you need to get the alternator replaced because the engine and cars computer system needs the electric output of the alternator to keep the engine running.
Some cars may not even run for another 5 or 10 minutes after you get it started with a dead alternator.
Some cars will run longer and others will not run that long.
If you turn your lights on then the battery may go dead sooner and the engine will stop and leave you stranded sooner.
I have ran a car with a bad alternator and only drove it about 1 mile and it was still running but I would not want to chance it any further than that.