Looking at them, yup; given they put the intro chapters to the 3E AP in there, certainly possible: on the other hand, I saw the Wrath of Ashanadalon (sp?) board game Barnes & Noble just before Christmas. Wouldn't surprise me if part of the original AP got translated to 5E and turned into on of their storylines, given the IP value.
The problem is the AP is kinda poorly done, IMHO.
Spoilers:
[sblock]The Sunless Citadel is great, and it does so the seeds for the Asharadon/Guthias/Dydd storyline well.
The Forge of Fury mostly ignores it
The Speaker in Dreams also ignores it.
The Standing Stones ties back to Dydd and the Cuckoo, but the adventure itself is meh.
Heart of the Nightfang Spire is a proper sequel to Sunless Citadel, as Guthias, the vampire priest of Asharadon that was staked where the Guthias tree was (and when you kill the tree, you release the vampire) is the main villain.
Deep Horizon had little tie in
Lord of the Iron Fortress is likewise mostly disconnected.
However, Bastion of Broken Souls DOES tie in the whole thing by making you face Asharadon once and for all. [/sblock]
So really, the only adventures that deal with the main plot is Sunless, Standing, Nightfang, and Bastion. Everything else is level filler.
(Cavaet: Its been years since I read/played any of them; I might be misremembering additional tie ins.