I don't think Eb will survive the BAT... I also believe that, at some point, Harry will be sent to get Mother Winter's cane back.
Eb, as Blackstaff, is allowed to use mind magic... We will find out that Eb rewired Harry's brain in Hog's Hollow after the incident with Justin. He has been asked a couple times why he does what he does and he doesn't really give a good answer - I think they were trying to clue him in that his brain was altered. I also think that Eb influenced Susan's thinking to keep Maggie away from Harry, since Eb was with them during Dead Beat and I doubt that was a coincidence.
I think Eb will succumb to the corruption of Dark Magic and the Outsiders, causing Mother Winter to send Harry after him.
Disclaimer: I have been wrong each and every time I have predicted anything. If I said Monday would be followed by Tuesday, I would expect the flow of time to suddenly change just to make me wrong. Jim Butcher has come up with better stuff than me every time I think I know what's going on, so I'm sure that trend will continue and I look forward to finding out how wrong I am.