Sure the trail is runnable. Originally, the Badwater Ultramarathon finished on top of Whitney (146 miles from Badwater), but now due to permit restrictions it finishes in Whitney Portal (135 miles). Still some of the Badwater runners get permits for that day and finish at the top. I know Scott Jurek did that a few years ago, but he's not the only one.
Running Whitney wouldn't be much different than doing the Pikes Peak Marathon, except it goes about 400' higher and the trail is 22 miles, not 26.2. The main Whitney trail is a very mild grade for going up a 14er. It's class-1 all the way. There's nothing class-2 about it. The only downside is having to carry a good bit of water. The rarified air is rather dry to say the least. Another 14er that's runnable is White Mtn (home of the world famous Bristlecone Pine Trees). People have ridden mtn bikes (and even unicycles!) to the top of that one.
