Well, that would depend on how old the gun is and if it's ever been cleaned of copper fouling. If it's a brand new gun, the barrel would need some time to wear in and there could be copper fouling in it, forming in any rough areas. If you've shot 200 rounds without cleaning, I'd clean it.
On the other side, if it's an older gun, for example, say something from 1978 (for sake of argument), and it's had 50 rounds a year run down it, that would be 1500 rounds, and it's never been cleaned of copper fouling, you can bet that there's a build-up in there. Probably a couple of layers of carbon, copper, then carbon, copper, etc.
If a barrel has any rough areas at all, it's going to grab copper from any round, regardless of velocity. People talk all the time about shooting a barrel to smooth it out, break it in, etc. Well, if there's a build-up of copper in there, continued shooting isn't going to do anything to smooth out the barrel, all you're doing is smoothing out the copper lining that's built up in there.
When you start with the Barnes bullets, you need to have a completely clean barrel. The pure copper of the Barnes is different that the copper alloys used in jacketed bullets. More than likely, if you don't start with a clean, copper free barrel, the build up of the alloy in the bore will strip copper off the Barnes bullets like crazy.
I don't really care for the ammonia solutions, although I admit that I do have a bottle of Barnes Copper Solvent that gets used VERY infrequently. I've found that it really only works in smooth barrels with little copper fouling. If you use the solvents, they will also eventually eat the bronze bore brush, since bronze contains copper. I just use a cleaning jag and lots of patches. Remember not to leave the solvent in the barrel for more than a couple of minutes, as the ammonia can etch the steel if left for too long, and that will only make the barrel foul even worse.
I prefer to use either JB Bore Paste (from Brownells) or the Remington Bore Cleaner (about $4 from Wal-Mart). Both of them contain a vegetable matter abrasive that won't harm the steel in the barrel, but will remove any kind of fouling from the barrel. The JB is a thick paste and it's more aggressive than the Remington. The Remington has a light oil base and it's a liquid. I usually drain a little of the oil out of the bottle to concentrate the particles. The Remington is easier to use, clean-up, and easier to get as well. It takes more elbow grease than the JB though.
Take a patch, wrap it around a brush, coat it with the cleaner, and brush it through the barrel 20 times or so. Then I run a clean patch through it, and repeat until I think the copper is gone. Now here's what I use the Barnes solvent for: After a couple of runs with the Bore Cleaner (or the JB), I patch all of it out of the barrel, run a patch soaked with the Barnes down the barrel, leave it for a minute, then run another lightly soaked patch with Barnes down. If it comes out with blue streaks on it, there's still copper in the barrel. Then I do the Bore Cleaner again, and then test again. The patches of Bore Cleaner/JB will never look clean, so don't worry about that. You can scrub a perfectly clean barrel and they'll still come out dirty looking. After you've got the copper out, run a couple of oiled or mild solvent soaked (Hoppe's #9 or something else) to get the residue out, then a couple of dry patches, then another oiled one to protect the bore. This sounds like it'll take a while, but honestly, it's a whole lot faster than the soak, wait, patch, soak, cycles of the Barnes Copper Cleaner.
Here's the thing to also remember. Most barrels don't shoot their best when completely cleared of fouling. After I find the load that I'm going to use, I rarely clean down to bare steel again. I'll just do a run of the Bore Cleaner/JB every so often to knock the fouling build-up down to the point that accuracy is still there (some guns will take several hundred rounds before accuracy goes, some won't. My Remington 7400 30-06 goes to hell after about 20 rounds), it'll only take 5 or 10 minutes if that, then oil it until next time. Then once or twice a year, usually when it's either really hot outside or really cold outside (times when I want to be inside
), I'll clean them down to the bare metal, break them down, etc. A really good thorough cleaning session.
Another thing that I usually do to any new gun I get is to take the Bore Cleaner/JB and run about 5 patches, 10 strokes each, through the barrel. Saves using ammo to "break in" the barrel, and it seems to reduced the fouling a good bit too.