Not really. In my experience, Ive seen alternators that put out fine amperage and voltage with no loads on, but fail when you turn on lights, fan, wipers, etc. Ive also seen it the other way around, low voltage/amperage with no loads, but good with loads. The internally regulated alternators are quite interesting characters sometimes.
Anyway, the fact the belt was sqealing may mean the belt is loose and slipping, which in turn wouldnt produce correct power, especially with a load on since that would make it harder to turn the alt, thus making the belt slip more. It could also explain the burning smell, since the rubber would be getting hot.
However, noise through the stereo is usally a bad ground (at least when installing stereos), but it could also be a bad voltage regulator messing with things as well. Ive seen that happen before too, peoples voices start going high pictched as you accelerate, then lower as you slow down, lol.
I would pop the hood and start checking all your connections ESPECIALLY anytime you smell burning. Check the battery itself to see if its hot after its been running (overchargning - cant really listen for boiling with a gel cell), check the positive side of the battery and where it connects at the starter (it could short out here), check the negative side of the battery and follow it to where it grounds, check that as well. Check the charge wire off the alternator, and check where it goes into the fuse block under the hood, etc.
While you're under there you might as well check the belt tension too, make sure its not too loose.
~T.J.
