Need to backtrack some before getting into charging system checks. I'm not saying a faulty charging system won't cause strange problems, as it certainly can. If you really suspect the alternator is your problem, unplug the small connectors to it or just take the belt off and see how it idles. My bet is that it will idle just the same. Ron had posted some very valuable checks that didn't seem to get much attention -
There are only two ways for air to be entering the intake on a healthy engine: one, past the throttle plates, and two, through the IAC motor. Remember that the IAC is simply an electronically controlled bypass of the throttle blades. First, you need to verify that the throttle plates are completely closed. Remove the large intake hose that comes from the air filter and make sure that the blades are completely blocking the throat of the plenum. If they are partially opened, back down the small screw under the throttle linkage until it is closed completely. Second, you need to verify that the IAC is not stuck open. Remove it, and you will see two holes on the backside of the IAC. Verify that the little plunger is not allowing air to flow between the two holes. Next, if the throttle plates are truly closed, you should be able to plug the holes on the intake manifold where the IAC goes (just use your fingers) and the engine should barely run, if run at all. It shouldn't be able to run without air. If you still have a high idle, or really ANY idle with your fingers over the IAC ports, you need to find out where the air is entering the engine.