If damage is assigned to AAA during bombardment, can it defend before general combat begins in the territory or is it removed?
On page 15 of the Axis and Allies 1942, Second edition rulebook, it is stated:


  "Roll one die for each battleship and cruiser that can conduct bombardment…For each hit, the defender will move a defending unit behind the casualty strip.  These casualties will be able to defend during the land combat step before they are eliminated". 


This means that not only does the AA gun in your scenario still get to fire, but so does the infantry unit that got knocked out by the bombardment as well, at least for one round of combat.  In addition, even if the lost AA gun didn't get to fire due to its destruction, the other still would, and the destruction of the first would therefore be irrelevant because in the description of AA guns, it says,


  "Only one antiaircraft gun can fire in a battle, no matter how many are in the territory". 


In sum, both of the destroyed units in your scenario would have the ability to fire after naval bombardment phase.