I've shot a lot of BP rounds in my 44 Spcl 1866. Yes, they do leave a lot of fouling in the carrier area due to the thick walled cases. I used full cases of FFFg BP and even tried 777 to get the most power, and the largest bullets I could find (255gr RNFP sized .430) to try to get a good seal, and tried neck-sizing only, but still plenty of soot. I did not try annealing the cases, as the fouling issue was really not that big a deal to me. It never hung up shooting a stage. On low humidity days the carrier would sometimes get sticky as I levered the rifle at the unloading table. A quick spritz of either moosemilk or just a mist of plain water would free it up again. Usually only had to do that once. So yeah, it took more time and Q-tips to clean afterward and was a bit messier. I only took it apart once every few years and the innards would be pretty gunky but still working fine.
These days I have rifles in a variety of calibers, and yes indeed my 32-20 and 44-40 '73's seal the chamber much better but I do not hesitate to shoot BP in the 45LC or .357 '73's either.