Yes. The engine tries to idle faster up in order to raise the voltage. Once your alt. is completely gone, your cary may idle really really fast when you stop. When mine went out, I pulled in the driveway and the engine started screaming so I turned the car off immediately - she just went full throttle trying to raise the voltage.
If all you are noticing is your car idling faster, then get it checked out before assuming its your alternator. You'll know it when your alternator starts going bad. If you have a voltage regulator on your car, then even a monkey could figure it out. If not, then your battery dummy light will come on before anything, and you'll eventually notice electrical components acting up, lights getting dimmmer, etc.