I think this could be part of Twelve Months, if Jim decides to make it so (or it might be deferred to another book).
Last I've seen the plan was still for Mirror Mirror to come after Twelve Months, which would start to add up to a long delay between BG and the feds showing up. My guess is Twelve Months at least touches on them, if only peripherally.
I suppose it's possible they'd recruit Tilly. On the other hand, it's potentially too easy to make the point of contact a fed who's somewhat sympathetic to Harry, after coming to believe him and teaming up against the Reds in Changes. The Librarians probably work better if they start off more antagonistic and it takes a real effort to win them over.
At a guess, I think the Librarians might be more likely to pull some strings to transfer Tilly to some dead-end backwater posting or surveil him (thinking him potentially compromised, either as a sympathizer or by mind control, after too much contact with the wizard) than to actually recruit him. I think there was a WOJ that the main reason Murphy never got an invite was that they were suspicious of her known association with Dresden. So if Tilly has a role in 12M, I'd bet in the direction of him helping / working with Harry on something isolated, then paying a career price for it to introduce the kind of pull the Librarians have. Something along the lines of an epilogue appearance to tell Harry some undefined other feds have been questioning Tilly's associations, and maybe he's being reassigned to the Wyoming field office.