In light of that theory does that mean that longer barrels in a .62 cal might shoot tighter patterns? Will a thirty eight inch shoot the same as a forty two inch or longer?
Depends. (no not the adult diaper.... ) A friend had a 20 bore with a 42" barrel that shot nice patterns. My 20 bore with a 41" barrel shot donuts untilll I got rid of the cushion wad, even then it wasn't the best. So in my experience, some 20 bores will and some won't but I suspect once you get out to 48" to 54" chances are they will probably pattern better.
I have also found that a "Nock-ish" type of chambered breech improves patterns as well, but I don't have but a couple guns that I have built and/or shot to prove that on.
The emboldened print is spot-on and coincides with the 'ratio' of bore size to barrel length. The longer the barrel, the lower the pressure at the muzzle, thus the 'potential' for better patterns.
My 32" Hunkeler 20 bore shoots beautiful patterns due to it's standard choke. I do poorly with it using ball. If it had a jug choke, I would expect it to shoot almost as well with shot as it does now, but perhaps shoot ball better than it does now.
Currently, it is a winning clay bird buster, shooting good modified patterns using 1-1/8oz shot and 75gr. 2F with only about .010" of choke.
The gun's English Styling feels good enough that if it had a .54 or .58cal rifled extra barrel, it would make a nice hunting rifle as well.