The mechanism with reducing muzzle diameter for threading to be concerned with is the bore opening up (reverse choke, bad ju ju for real accuracy). But the overwhelming majority of barrels that get threaded aren't accurate enough to know the difference. I doubt one AR in a thousand is that accurate. They don't normally start out with large muzzles to be reduced very much either. It's real though and why you wouldn't want to take any more diameter off the muzzle of a precision barrel for threading than necessary. It's why I went with a CB mount so I could use the same can on threads from 1/2 to 3/4, sparing my heavier barrels from being reduced to 1/2.
The harmonics thing is obviously separate, but can cut either way - if it can improve, it can also degrade. Tuners definitely work. Hanging a can is hanging a non adjustable, one setting tuner. It WILL affect harmonics. Period. Your barrel and load might like it, but it might not. Luck of the draw. Of the five centerfires I had threaded, none got any better, but a couple got worse and needed loads re-tuned. One was easy to tweak the load and get back where it had been. The other, I have not been able to get tuned back to where it was before being threaded and having a can hung off it. Now not totally sure it will ever get back with just load tuning, but if it does it's going to take a completely different new load, not just a powder or seating depth tweak. It was the most accurate one of the five, to begin with, naturally... Again though, I think the majority of barrels and loads that go this route, aren't accurate enough, or at least never get shot in a way to know the difference anyway. It's not the kind of thing you'll know about by shooting a couple three shot groups.
Concentricity of the whole job and quality of any re-crowning are important too. Crown doesn't get touched while threading unless the barrel gets chopped, then it needs re-crowned. Possible to screw it up, obviously, but anyone I'd trust to thread, I'd triple trust to crown. I'd be most suspicious of factory threaded barrels.
To the original question "DOES it HURT accuracy?". Impossible to answer. It can, for sure. Couple different ways. Done properly and intelligently, it isn't likely too though.
It really can't do anything to help accuracy either though. Simply can't. There's no plausible explanation for how it could (assuming a crown wasn't bad, but that would be obvious before starting). When you see noticeably improved accuracy after threading and hanging a can, you didn't have a very well tuned load to begin with and just got lucky on the harmonics and the non-adjustable tuner you just hung. No mystery.
- DAA