Again, Burgess HAS DONE this before just not extensively. By your standards, why did the Pats trade a fourth rounder and play Ted Washingon (a career one gap DT who never played 2 gap NT) at NT on first and second downs. Washington spent his entire career playing a one gap where he did similiar things that Burgess did only on the inside (try to pentrate to make plays) and then came to the Patriots in mid August and immediately asked to play the two gap and tie up blockers. He did it and now you are saying Burgess can't.
I agree that they won't use Burgess as they used Vrabel. First, he doesn't have the coverage skills. Second, the Pats have far more depth than they have had in several years. Belichick likes to have a rotation at OLB like he did in 2004 with McGinest, Rosie, and Vrabel. I don't expect Burgess to be in on every down or the majority of run downs, I just expect him to be out there more than you think.
As for the one gap, It is sometimes harder to shed a block than engage one because when you engage a blocker to tie him up.
I still don't get why you are so hung up on this "he hasn't done it for his entire career" considering the Pats have been pretty successful in bringing players like him in and getting him to play fairly well in a position they have never played (Ted Washington, Junior Seau, Keith Traylor, AD at least at ILB, Eugene Wilson who changed to safety the second week of the season having never played the position). Most of the failures at this have been guys who weren't very good to begin with (Monty Beisel).