Hmmm, not really. The Major Dia is the o.d.
The wires make contact WITHIN the vee. The wires are not affected by the crest height.
Yes, engagement will suffer if you end up with very flat topped threads. .125 x pitch is book on crest width.
Consider this: 1/4-20 2A bolt Maj Dia runs down to .2419. Your 1.055 squeaks in.

One thing I finally realized into my apprenticeship is that a 20 tpi/pitch has .050 from crest to crest, the depth to the thread root is the same, No Matter the Diameter..... all 20 pitch threads have the same basic numbers whether wrapped around the quarter 20 or a telephone pole.
Overall dia needs to be added, of course, but, the pd tolerance for a class 2A 20 tpi will vary but .0037.