Thanks for you interest, regarding your questions:
Yes it could, the PID being a linear system, could also be “indentified”. Actually you can exchange the input for the output column and viceversa, and a model will come up trying to match the controller dynamics.
But only some common process models are supported by the tool. There is no “PID model” built into the software, so you won’t be able to “recover PID gains” from data with the software as-is. It could be done, but there no common use case for that, so it is not worth development time for me.
The most common case is what is presented, model the process, then use the model to obtain good PID gains as a good starting point for tuning the control loop.