rdautogallery is correct. My car was dying in the middle of the night, lights getting dimmer, etc. so I pulled off to the side of the road until daylight. It turned out is was a loose fanbelt. I tightened everthing up and fortunately there was enough juice left to get started. Without the alternator the car will not run. At least with a generator the car can be push started; not so with an alternator. Check the fan belt first then remove the alternator and battery and go to a major auto parts dealer. Most will check the alternator and check/recharge the battery for free. Check and tighten all connections; I once had a connection to the alternator post that was falling apart but the problem was hidden by insulation.
the big answer is yes and no. your battery can power your engine however it gets charged from your alt. Now if your car has a full battery and alt stops working you can keep driving it for as long as your reserve goes. your battery is 12 volt but if full puts off 13 to 13.5 volts. now your alt puts off 14 to 15.5 volts. So your see dimmer lights with less volts as well. will not effect spark much, unless your battery is almost dead.