Saving data to device with parse

Planning to save data locally, I have created a ContentProvider backed by a SQLite data base. But now that I am deciding to use Parse instead of App Engine, do I still need my own SQLite-ContentProvider to persist data locally? Or can I configure Parse to fetch some data to the device so user can have offline access? And by offline, I do not mean in-memory: I do mean available even after the app is destroyed: sqlite style.

With App Engine the server would use an algorithm to decide what data to make available offline (for argument say its “trending” data). Can I still do that with Parse? My whole ContentProvider is already created and paired with an SyncAdapter so as to sync the “trending” data periodically. How would something like this work with Parse? I want to take full advantage of the conveniences of Parse, so I don’t really want to do things Parse itself can do for me. I hope the question is clear and is not too much for a response. Thanks.