Basically structure is the same, but I'm afraid Hexen2 has a modified version of Quake engine. You can't just load it as a mod, but it should be easy to convert it.
Anyway what's the point of doing this? :) 

I think I need to stop doing re-makes! :P 

I imagine that there is a metric arseload of little things that add up to it being a lot of work.

Off the top of my head, one big difference is that H2 is hub-based, like Quake 2, and getting all that persistant-state-across-multiple-maps stuff working in Quake would be a ballache.

Another thing is that I believe H2's entity thinks happen 20 times a second, rather than Quake's 10. That's gonna cause issues I imagine. 

Hexen 2 has a lot of extra gamecode using extra engine builtins. It would be a large project needing a lot of programming from different people.

I have an unfinished Hexen 2 map that got shelved because it broke the extremely low clipnodes limit. It wasn't clear to me while mapping that H2 has a much lower limit than Quake. When I learned the reason for the problem, I lost interest in continuing because what's the point if the map can only be 1/4th the size of a Quake map. There is the hub system but that still is very limiting.

Eric's tools and Spike's engine now support BSP2 for Hexen 2, which makes it theoretically possible to continue, but tbh I don't want to rely on FTEQW exclusively for this. If Hammer of Thyrion got BSP2 support, then maybe. But when I spoke to Ozkan Sezer about BSP2 a few years back, he didn't exactly seem thrilled by the idea.

There is also little interest in Hexen 2 maps. I've also seen a lot of dislike for the H2 monster lineup, and that's partly understandable - the skull wizard seems everyone's favourite but archer knights are really pretty boring. And I'm not a fan of the Aztec and Egyptian stuff myself. And the key items are hardcoded IIRC so it's not trivial to make your own unless you want to hack the gamecode.

There's also no good editor for Hexen 2. It's possible to use Radiant but you have to manually convert the .map files. and IIRC there is no real .def file. Divining the entity names and keys from 20 year old internet pages or from the code is annoying.

I don't think porting the entire Hexen 2 to the Quake engine would be a worthwhile project. It would be a giant pointless slog. Also some of the interesting monsters are in the expansion, so you'd have to port even more.

Not to mention legal issues of course. Similar problems to porting entire chunks of Doom etc. to a Quake mod. While no one might immediately sue you, it's still not exactly clean.