No, it's quite well defined, and it's not called a 'memory subsystem'. There is a training process (as in traditional Machine Learning training) that occurs with data available at the specific point in time the training starts (or ends), this is called the cutoff date.

After this point there can be other kinds of training, the weights can be shifted, the internal CoT prompts can be changed, routing in MoE can change, but the Foundational Model that was trained on a corpus is the same model trained in the same corpus.

User data can be used at any of these stages theoretically of course, but by the nature of training and from the dates of the events, (a new Foundational Model being released), it would look as if the user data of the professor was used in the training of the foundational model, which is something that OAI does every couple of months for a big release, and incorporates the new text from their text scraping efforts, including new books ingested, new internet text scraped, deals with third party platforms, and data from their own users (not conjectured, read the ToS, users allow this.)