Is it possible to create a bookmark in the Google Docs API for a specific paragraph element and then get the bookmarkId of the bookmark?
Unfortunately at the moment this isn't possible to do.
Google's Issue Tracker is a place for developers to report issues and make feature requests for their development services, and a Feature Request for this has already been made over there.
You can view this feature request here, to which you can click the star (☆) in the top left to let Google know more people want this feature to be implemented.