A car should run just fine without the battery once you start it up assuming the alternator is charging and working properly.
In fact that's a good way to test if your alternator is working properly and charging.
You can easily check your alternator to see if it's charging by starting the car and let it idle while you remove the battery cable and if it dies then the alternator is bad but if the engine stays running once the battery is disconnected then the alternator is good and charging.