A bad alternator could cause your battery to not charge or could drain your battery and that would cause your car to not start.
But just having a bad alternator won't prevent your car from starting.
Your battery, loose connections, bad starter, bad starter solenoid are things that would cause your car to not start and just click or do nothing at all.
If your cars engine does turn over though when trying to start it then that is something else such as bad ignition coil, bad distributor module, bad spark plugs etc.
If your battery keeps going dead then you should have the battery checked as well as the alternator.