Copper fouling isn't a problem when shooting jacketed bullet, only. But a little residual copper fouling that is almost imperceptible can make lead fouling much worse. I've gotten this kind of fouling from shooting factory UMC ammo, before. The "FMJ" was evidently just a thin copper plating. Copper fouling turned into lead fouling, as the crappy bullets were being torn all the way through the plating. Turned my Glock 21 barrel into a mess. This was before I started reloading.
A quality bullet like Berry's, you won't have any issues with. But after extensive shooting with any jacketed or plated bullets, it's a good idea to thoroughly clean the bore before going to lead. Not necessarily needed going from lead to copper, though; if it looks clean to the eye, you'll be fine.
It's not uncommon for a pistol to lead up really bad the first time you shoot cast bullets. But after the first thorough cleaning, it stops. This is suspected to be because the first thorough cleaning removes the copper fouling that you've had in there all that time.