I've found a problem with having tame sheep. The moment I pen them up to do anything with them, instead of being stressed out, ours start thinking "hmmmm, this is boring. I know, I'll start cudding".
So, whilst it's a bit messy, it's far from disasterous. However, if I drench into a mouthful of cud, will it still go to where it needs to, do you think?