I don't know. There are a lot of early fights where the PC (if using HotDQ as written) would get swarmed by foes. Plus, there are about 8 early fights. It's the same issue that PCs have against NPC solos. Action Economy just goes heavily in favor of the NPCs in a solo HotDQ. And class would make a bit difference as well. The PC would quickly run out of hit dice if he takes one or more short rests as well. Sure, a Wizard might fireball a bunch of mooks and win a few of the encounters that way (ditto for a Cleric with Spirtiual Guardians), but there are some classes like Rogue that would be toast.
I think it would be doable but extremely difficult depending on build.
If I were the player, I'd probably focus on making an uber-Stealth monkey and try to avoid combats with multiple opponents. Either that or I'd make a character with maxed out AC and hit points.
If I were the DM, I'd probably make sure not to overwhelm the PC. Either that or I'd give them a team of NPC followers like in most solo-oriented CRPGs.
It's an interesting idea, though, Zard. From what I've seen of Out of the Abyss, it sounds like it could be fun to run as a solo adventure as well.