Is "persistent cart session" in fact checkout/session or is it a separate session? If it is separate, can I use it from my modules? I need some data to persist together with the shopping cart content.
If you need data to persist with the shopping cart session, extend the shopping cart. No need to piggyback on the customer persistence.
If you need data, you can extend the following tables -
sales_flat_quote_item to inject your domain-specific logic into the sales. The persistence module should resurrect the shopping cart session as per usual - only associating it to customers that have logged in / performed actions on different devices.
Persistance is also limited in CE. Wishlists and more aren't available in CE, only in EE. In CE 1.6 / EE 1.11 it was unable to work with compilation. I'm not sure if this was addressed in later releases.