Sounds likely.
In trying to save themselves, they saved most of Boston.
Too bad Boston was too tied in to the rest of the county to fully survive it's demise.
Just in Time supply systems are a [censored] for natural disasters and nuclear wars.
Having all the manufacturing capacity in the world does you little good if you only keep 48 hours of parts on hand and your suppliers are located all over the country.
And grocery stores are nearly as bad.
Add in starving refuges from all over the New England area likely dying from radiation poison...
Plus any bioweapons the Chinese sent over.
Raiders fighting over the remains....
I'd expect any surviving military forces to rally to Boston, but maybe they did then became part of the Institute.
Military Science Department of course.
I'm interesting to see how detailed Bethesda is on how Boston got to where it is 200 years after the war.