If you loosen the alternator to remove the belt, how do you plan on tightening the belt once you place it back on??
Just do it the right way and loosen the big 17 or 19mm (forgot which size) bolt that goes through the heart of the tensioner about a half turn, then loosen the tensioning rod (13mm) a few turns to lift up the pulley.
Installation is reversal of removal
:p