My rabbits haven't been sick (knock on wood) and you know how I am about trying to keep things sanitary, but yes it is entirely possible that show rabbits can be exposed to illness and stress can weaken their immune system, too. I enjoy the shows, but there is always that concern lingering in the back of my mind and although people aren't supposed to bring ill rabbits, it happens from time to time. I keep hand sanitizer around and now I try to set up near trusted friends. Unfortunately where there is little control is on the actual show table with the judge because it has seen many rabbits and I have never seen a judge use anything on their hands between rabbits. Since I don't attend a lot of shows, when I do go to one I do a mini-quarantine after to keep an eye on the show bunnies for a few days. Any new stock also goes into strict quarantine for at least a few weeks separate from everyone. I only have a small group compared to some, but I have put a lot into them and I just do the best I can to keep them healthy and happy.
Fortunately I haven't had to make a decision like this, but as I am also trying to breed for good health and part of that is being able to have a strong immune system. Unfortunately if I did have a snotty bunny after a show (ie pasturella) or any other serious health complication, I would most likely opt to cull(euthanize in this case since I couldn't just give the problem to someone else or risk spreading it further) for the safety of the rest of my gang. At the shows themselves, I use my own carriers of course and I typically keep hay for the buns to much on in with them along with water from my house. This seems to help minimize stress and having handled the rabbit frequently and socialized them to day-to-day things like loud noises before the show will help also because they are desensitized to being picked up, posed, hearing different things, etc.
Here is an article on rabbit stress and disease at shows:
http://www.lopsandcavies.com/showing/sh ... isease.htm
That said, I don't think you should be overly frightened about showing, especially if you might be interested in breeding at some point. I learned so much at shows on what areas I need to improve and even picked up tidbits about breeding/health/color/raising/etc. from listening to the judges comments, other respected breeders, and have made bunny friends there, too. Pie and ET have a very similar temperament and ET is really not fazed by shows really at all. He has been to at least four or five off the top of my head and he just kinda hangs out while he is there, is tired from all the excitement the night of the show, and then is back to his old self by morning.
Lauren