There is not a way to use the new GUI for the connection manager in Processbook 2015 R2 SP1. I'm right there with you that it would be nice to control both AF and Data Archive servers from a single window in Processbook like is possible with DataLink and PI System Explorer.
I took a look through User Voice to see if anything matched with what you're looking for and the closest I came up with was requesting consistency for the tag Search functionality of OSI's client tools. I would recommend you leave a comment on this and mention that it would be beneficial to also have consistency in the connection manager's across the client tools as well.
Thanks a lot for the feedback Robert, I followed your note and make the statement in the Feedback Site.