Yeah it is 100%, just like the other timed runs I suppose. For Bronze drake & ZA bear only one would drop as well and everyone would roll. Only now it's personal loot so the person that gets it is already determined - I assume it's trade-able though like most personal loot.
Could definitely farm it with some friends or guildies over a 5 week period to get everyone the mount, but since I'm always left to pug it that won't be an option. Regardless, a 1 in 5 chance are much better odds than I'm usually left dealing with..

and if the drop rate remains unchanged once Nighthold is out I'll probably start farming it regularly. Considering normal Nighthold alone drops 870+ gear it won't be hard at all to power through Karazhan in a couple months.