You may need to contact the local code enforcement or insurance people
to determine what they want. Just adding GFCI will not change many of the
issues some areas and regulations have with K&T.

Actually, K&T wiring is pretty good stuff!

It's reasonably safe even AFTER the mice have eaten the insulation as the
"real" insulation is provided by the knobs and tubes.

A GFCI on a K&T circuit would protect the circuit from any significant
leakage to ground. The basic nature of K&T is that "shorts" between the
two conductors are very unlikely but anything from a nail going to far into
the wall to a broken insulator might cause contract between a conductor and
some other metal object.

Obviously, you have to do whatever the local authorities and the insurance
company demand but when it comes to REAL safety, a GFCI will do the job.
Just don't forget to TEST the GFCI once a month or so.

If your GFCI doesn't reset, you may have to tear up the walls anyway but the
most likely place for problems is at switches, fixtures, and where you
transition from "modern" wiring to the K&T.