It doesn’t matter either way if he’s got them and you don’t you’re going to lose.  Therefore the purchase of AA guns is irrelevent.  Obviously if you’ve developed Heavies and have some extra cash then AA’s can be bought, but remember that someone with Heavies is likely going to target your factories so that you cannot develop this tech yourself.  Once he can eliminate that threat the game is over.  In other words you need to develop tech while you still can.