The process is widely used in a number of very technical manufacturing fields. What I've heard from most of those adherents, is that it makes a noticeable difference in how the material machines, or other properties that are useful in the manufacturing process.
Once it's made into a barrel, however, it doesn't seem to offer any tangible benefits to those of us who are merely using the barrels. In a side-by-side blind test with a control barrel, it resulted in absolutely no discernible difference in accuracy. This was based on a series of ten, 10-shot groups fired from each barrel, both before and after the treatment. The ammunition was all from the same lot of bullets, powder and loading session, without my knowing which of the barrels were treated (by three different cryo facilities, incidentally) and which one was the control barrel. All of the barrels were Harts, purchased at the same time and from the same run, specifically for this test. They were identical as we could possibly make them, and the groups fired showed that we were pretty successful in matching them up. When I cleaned these barrels, I did them all at the same time, and in exactly the same manner. Inspection with my bore scope gave no clue as to which ones were treated and which one wasn't. No difference whatsoever in how they cleaned. In the meantime, all of these barrels were used in our regular QC rotation, firing 168 and 175 grain bullets for daily production testing. As each barrel hit the 1,000 round mark, it was pulled and set aside. Once all had the same number of rounds on them, I again repeated the original ten, 10-shot groups from each, using the same control ammo. Ditto for cleaning and reassessing the fouling/erosion conditions, etc.. Still no difference. This process was repeated every 1,000 rounds until the barrels quit shooting and had to be retired. It's been a while, but I do recall that all barrels quite shooting within about 500 rounds of their mates, essentially no difference in longevity between them. Ted Lancaster revealed to me which of the barrels were treated, and which was the control once the testing was completed, but there's absolutely no way I could have told you by simply looking at, or shooting them. So, while it may well make a difference in how the material machines or forms, it didn't affect the attributes that we need as shooters of the finished products. Lot of rounds down range in that one, and it was all pretty rigidly controlled from start to finish. Bottom line is, no, I won't bother sending a finished barrel off for the treatment.