I've browned lock parts, trigger plates etc with plum brown. I try not to get it on threads or screw holes but if the part is oiled right after Browning it won't hurt anything even if the threads get browned. I go out of my way though to prevent plum brown from getting into the rifling. That's the last place I want rusted.
X2 on with Sidney said. Also, if it does get in the barrel, it is such a thin, controlled rusting, it shouldn't cause a problem. Just clean it up and oil well after application. In my experience it takes several oilings to stop the process in tight areas even after rinsing several times. As an example around sights on a barrel. I just use motor oil to initially oil the firearm to stop rust and get penetration into the browning.
If you do use Plum Brown, be sure the metal is absolutely clean with no oil, grease or wax on it. This includes fingerprints.
The metal must be heated to 285°F for it to work right. If it is much cooler than that, it will leave copper plating on the surface. Copper plating will keep the steel from browning so if it happens it must be removed by sanding it all off.
If the temperature is much hotter than 285°F, the solution will boil off leaving spots and streaks. In any case, even when it is working right, it will leave a crusty formation that must be washed off with water before you can reheat the part and apply more coats. It usually takes at least 2 coats to get an even looking browning.
I do use it for small parts like a lock plate or trigger guard. I quit using it on barrels years ago because it is difficult to get an even looking brown on large parts like that.
When you've got an even coat of brown on your part it will look much lighter than when the process is finished so this last step is important:
After the final washing and drying of the part, apply a heavy coat of oil to the surfaces. Motor oil, 3 in 1 oil, or any other kind of petroleum based oil will work fine. Let it set overnight to soak in. The next day, wipe off the excess oil and your finished.
Zonie is right on getting the oil off. I've had decent luck using brake cleaner to degrease a barrel. I also were vinyl or latex gloves during the process to avoid hand oil on the part. I have used a coleman gas stove or a propane torch to heat the metal. I started browning when water sizzles on the part. It usually takes 3-4 applications to get a decent brown on a larger part.