Hey Tim,
Unfortunately that is not possible. The buttons in JCE editor can only be used add contents into the post content, so they cannot be used to select the post cover.
However, you can set the 'shared media' to use the media content directory. The downside for this is, you cannot see the image thumbnails in the media manager because those image files(not uploaded from media manager) do not have thumbnail or other variations(
https://take.ms/BCb0I).
Also, 'shared media' means that all bloggers can see this directory in the media manager, which also means they can access the avatar image of other bloggers, if they are in that directory.