Yes, as Prospero has already indicated, the layout of T3 does not separate arriving and departing passengers. So you would certainly be able to reach the AA lounges in T3. I have a feeling that a strict reading of the access rules would not be in favour of allowing you access but I would have thought that in practice you wouldn't have a problem.

This is of course only if your arrival is to T3. If your arriving AA flight is from outside USA/Canada, you would arrive at T5.