Actually, it sounds like the current underground stuff is going to attempt to accommodate adventurers, kind of like cliff smoothing:
The bottomless chasms and pits are gone right now. HFS might involve them, who knows? But in any case the vertical connections will all be finite (haven't done them yet), though before climbing we're aiming on making most or all of the adventurer accessible.
So you should be able to explore them, although they still might have to be breached by a fortress.
The combat is also likely to feel quite different in Adventure Mode. The new descriptive paragraph generator will presumably be used for creatures that you examine. The entity positions rewrite, and the new goblin leadership thing, may have some impact on how adventurers get quests. If your civ is friendly with a goblin civ, you might find yourself taking orders from some non-demon megabeast.
I don't think there are any changes aimed exclusively at Adventure Mode, though.
edit: oh, also there's this (emphasis mine again):
I'm more curious about this world-spanning underground-layer ability. Will adventurers be able to get down there and roam around? Preferably with fast-travel, unlike the current tunnels?
You'll be able to get down there. I'm ambivalent about fast travel -- clearly, something is needed, since it takes a long, long time to move around. However, most of the feeling of discovery and exploration and some of the feeling of lurking danger is lost by allowing fast travel in places like that. There are some tentative solutions, I guess, like allowing fast travel in areas that have been explored or at least talked about, or change how the travel screen looks underground to make it look more intimate, but we haven't thought it through yet.
Can we expect some of the new cave systems to follow their geological tendencies - for instance high drainage areas over limestone? Perhaps something like the caverns and watering holes throughout the Yucatan peninsula.
Most likely not at this point. The principal goal of this underground update is to improve the fortress progression and adventure mode at a structural level, independent of atmosphere considerations (which are important but can't come first chronologically).