I Parkerize quite a bit here in the shop including a lot of barrels and I don't plug the barrels for that part of the process. (They are plugged for most of the other stages) When they come out of the tank, they're rinsed and the bore cleaned.
The Parkerizing does not "take" on the insides of barrels because the bores have not been abrasive blasted. Parkerizing does "not like" un-abrasive blasted metal.
The acid is relatively mild as far as acids go. If it get's on your skin, it burns right away because it's hot. It takes a while for a chemical burn to start. (The eye is a whole different story!!! That's why I have an eye wash station at the sink)
Truth be told, I have on several occasions wondered if the bore gets cleaner from the Parkerizing bath. I have cleaned a rifle bore and then Parkerized it. Afterwards, I cleaned it again and it's even cleaner now and brighter. My guess is that the built up lead and assorted other gunk is getting disolved by the acid. Keep yer powder dry, Mac.
Tuff-Gun Finishes. The Name Says It All.
Mac's Shootin' irons