Yes, paid airport upgrades (sometimes called kiosk upgrades) with AA do not earn anything extra (beyond your originally booked ticket) with BAEC or Aadvantage.

If you want additional TPs with AA you will need to do a fare class upgrade which essentially is a buy up from the fare you currently have to an F class ticket. Your ticket gets reissued as an first class ticket -- this often will be much more expensive than an airport kiosk upgrade.