According to the docs it's supporting iBeacon specifically. No mention of EddyStone, but a software update may very well add it in the future.
RFID tags are very cheap, and are passive so they don't require a battery, but they have a very short range, that's why the big antenna panels are needed near the exits.
BLE beacons on the other hand will be more expensive and have a limited battery life, they do have more range.
I'm afraid that for those reasons, for your use case, BLE may not be the right choice.
If you do decide to go forward with it, you'll need 3rd party software (a server) to interpret the data from the scanning API. No need for separate BLE readers. The APs can track the location of tags.
The scanning API also has a delay, which makes it even less suitable for anti-theft purposes, by the time 3rd party software receives the information from the scanning API, the thief will likely be long gone.