I don't believe that this information is accessible via session, cookie, etc. The current page is stored internally by the objects that control navigation through the survey, but this information is not externally accessible.
That information is stored in the database, in the ckbx_ResponseLog table. That table is essentially a "stack" of visited pages keyed by response id. I believe that the current page for a given response would have a started time but not an ended time.