A belt can be installed wrong/backwards but if that's the case you could not run it backwards because the engine runs the same way no matter what. The alternator does not determine the rotation. The engine determines the rotation of the alternator; therefore it cannot run backwards. An alternator running backwards would not only overheat it but would in all likelihood blow the diodes.

Assuming it is a serpentine belt system, it is possible for the alternator to run backwards. It is highly unlikely that one could be installed incorrectly however. Whenever a pulley is contacting the smooth side of a serp. belt it is spinning in the opposite direction of the crank pulley. I may not be correct, but I would imagine that the alternator would be fine. The one major issue I see, would be the alternators cooling fan being spun backwards causing it to overheat. Which would only be a factor after prolonged use. On a vehicle with a serpentine belt system, (one belt drives all accesories) all it would take for the alternator to spin backwards would be for the outside of the belt to contact the alternator pulley. I will provide you an example: Two pulleys in a vertical setup and a belt "around" both, the bottom being the crank pulley, rotating clockwise. The top pulley will obviously rotate clockwise as well. Now lets take this a step further. On the left side, in between the two pulleys the belt is moving up, and down on the right side. If you were to add a third pulley in between the two pulleys pressing against the outside of the belt the upwards force of the belt will rotate the third pulley in the opposite direction, counter-clockwise in this instance. An instance where this can be applied would be a vortec engine equipped blazer where the water pump is rotated in the opposite direction of the crank- called a REVERSE rotation waterpump.