With C16 collets that we use here at LRI we've experienced very minimal surface inclusion. "Sock it" and run. We've done over 200 threaded muzzles to date this year. So far so good. -I had to look it up.
If in the rare circumstance it was to mark it up, I have park tanks.
Regarding chucks: It's going to be a case by case basis. There are procedures that will mitigate surface inclusions. Its all relevant to the equipment, the process, and the skill set of the person setting it up. Often copper rings are used as a tangent point contact device for the barrel. These work, however the copper is much softer than the steel on the jaws/barrel. Its not uncommon at all for the copper to burnish into the surface finish. Especially on something like a parkerized finish because it's "toothy" from the media blasting and crystalization buildup on the substrate. While you barrel won't have a scratch in the steel, it can very easily have a copper ring burnished into the finish. Removing this kind of discoloration can be challenging. In truth its a real bitch.
Collets can do damage as well. No so much to the steel, but it burnishes the parkerizing and leaves a glazed look to it. It's stil there, just "knocked down" per say. Much like sanding primer. It's typically "fuzzy" when applied. When you cut it with 600g paper it glosses up.
Fixturing finished parts for post finishing machine work has always been a big challenge in manufacturing. Even stuff like DLC can be marked up pretty easily. I realize in this case your altering a finished product you bought "ready to run" so you more or less take what you can get.
The lesson here for the masses is to do a thorough job of planning your projects well in advance. This way shops can adhere to the order of operations so that the outcome is predictable and desired.
Hope this helps.
C.