A "fat" AP is called an IAP or Instant AP. In the past, if an access point did not have a sticker that said IAP-<model number>, it could not be converted to a "fat" AP. These days, the latest APs are all UAPs, which can be converted back and forth between IAPs (fat) and Controller-configured APS.
Look at the sticker on the back of the AP and see if it says IAP- or AP- before the model number.