This has NOT been my experience, but that's simply because I don't do it, haven't tried it. I either shoot any lead after I shoot my jacketed, or more often, I typically stick to one or the other in each of my guns.
In most of my handguns, I'm slinging cast lead almost all of the time. Not 100%, and for the times I'm doing both, I simply shoot all my jacketed first and leave my lead for later.
Removing lead from a barrel can be done in a number of different ways, but when I've leaded up a barrel, I've mostly done it with a tight jag, a thick patch and a LOT of repetition and hard-ass work. Elbow grease. Not only is it a lot of work, but you learn QUICK not to do it again if you can help it.