Not yet.
The vehicles are lacking a variety of hardware updates needed to enable true FSD. So that is a real problem current owners can not receive OTA. Tesla did not sell the right to have those cars upgraded at no charge–or at all. Otherwise, every Tesla buyer would get a “current” vehicle whenever it was necessary to update the vehicle hardware (not just the software).
In other words, Tesla is exactly like any other auto manufacturer. You get this car now, and some cheap upgrades (OTA) in the future. You do NOT get any needed hardware updates–nor will they promise the car you bought can take advantage of/use all the OTA software updates to be released in the future.