In theory autogranting doesn't affect your banked AA, in reality there are interactions which I experienced myself. One example I experienced is that the granted AA caused several of my banked AA to be removed. I had max banked AA, I didn't play EQ for a while, and there was an EQ patch that reset an AA due to a change, so people were given back the AA. Since I didn't log in for a while, those AA were autogranted AA that were then given back to me to my banked AA pool, but since my banked AA pool was full, and I didn't spend them on time (since I wasn't playing EQ for a long time), those AA were lost.
That was a one time thing because of AA consolidation from a patch, not from autogrant. The answer to the OP question is no, autogrant doesn't use banked AAs.