My friend and I tried with prot warrior + fury warrior. Even tho i had trinket to sustain damage, flasks, around 46k health and tons of defense + stats. It wasn't enough to surpass all the damage bosses give... The 2nd boss if you go from the horse guy, is a rogue that gives you infinite bleeding. That bleeding deals around 5k damage every 5 seconds and it's insane amount. He has around 400k health so bursting him is pretty hard even as furry. Not to mention that if any mob/boss attacks my friend, he dies in seconds as they burst him quite fast.
We managed to get to Opera event (it requires all bosses done before) but we were unfortunate to get Julia and Romeo... they are hardest there to kill and it's nearly impossible with only 2 people, literally impossible as it requires tons of interruptions and to kill them at the same time or they respawn again. Then later on when we found 2 more people, we managed to get all to chess part but it was freaking bugged as hell. Enemy warlock was shooting bolts from insane range, priests could heal even tho they are out of range which makes no sense at all, nothing was working as intended...
But I saw videos that chess part can be done even with 1 person there, so IT is possible to solo Karazhan but only if you're playing Cataclysm or something. I don't find any class in wotlk being able to do so because of tactics/bleeds/arcane damage/ no heals,etc. Maybe unholy dk mainly of heals but I doubt he can as well.
Also Sathrarion is nothing impressing, there are already guides where people say it's possible and he is playing dk who has heals so...