Yes, Dworshak has good numbers of elk, and you would have a good shot at harvesting one. There are plenty of hunters there, but you can get away from them if you're willing to do the work of hiking way in before dark, or if you can stalk in some tough, thick terrain. Incidentally, that's where the bulls are anyway.
I always tell people that are coming from out-of-state to decide what kind of terrain they want to hunt in, and ask themselves what kind of shape they are in. The terrain changes a lot in Idaho. You can hunt in Dworshak and feel like you're hunting in a rain forest. Some people hate that. Or you can go further south and hunt in the high desert mountains.
Either way, there's elk all over. But that's why I tried to talk not just about elk numbers, but also about terrain in the series of posts that I linked to earlier.
You can find places to camp in the Dworshak Zone - no worries there.