I think the Vau N'Akat seen in Prodigy have a lot of "biological and technological distinctiveness" to be added to the collective's own. My question is whether or not the Borg could take advantage of the Vau N'Akat's abilities, and whether they'd be all that helpful.

For instance, could assimilated Vau N'Akat use their heirloom powers to manipulate materials in order to pump out at least the shells of Borg Cubes like nobody's business?

I think this depends on how heirloom material actually works and is made. Its utility to the Borg probably depends on whether or not it's a limited resource or actually some sort of alloy that could be constructed anywhere in the galaxy.

In truth, we can't know that, as in the current state of canon Vau N'Akat lore, it's basically just space magic to us. If I had to take a wild guess, I have two theories:

1. Maybe Vau N'Akat have detachable nanobot-esque cells that communicate with the brain over an electromagnatic signal, allowing the quick assembly of structures at a relatively precise level, especially with the one specific material. (Perhaps all that blue dust stuff that happens at death are these cells freaking out as communication ceases and, for lack of orders, devouring the body.)
2. The Vau N'Akat have organs that essentially very precisely accelerate exchange particles. (This theory makes the above one seem comparatively more plausible.)

Another question is whether or not Vau N'Akat drones could use all that "your will is mine" stuff to aid the assimilation of other Vau N'Akat and/or create one super drone.

Going with theory 1, maybe the "Your will is mine" stuff is actually a weak ability to lend extra cells to the desired person that builds up when a lot of people are doing it, strengthening healing and immune responses as well as any use of that person's detached cells, thus explaining that whole scene.

If this is the mechanic by which it works (and assimilation doesn't somehow bork the mental facilities for this), this could be a very powerful ability for the Borg. It almost sounds too powerful, as those cells could be used as essentially an assimilation virus or a bioweapon, which I think would break the balance of power in the ST universe in a way that I think writers really wouldn't want to.

Overall, as I have said before, just as I find it very fun to try to theorize how the Vau N'Akat work, I also find it very difficult due to both its status as a very new species and their general uniqueness (almost un-Trekiness, not to insult them) as a species. I do think Prodigy does some good things with the Vau N'Akat, and it's nice to have a species that's a bit more than just forehead ridges and a fatal flaw (if they even bother with the forehead ridges - looking at you, Betazoids). However, similar to some of the complaints with Prodigy in general, I can't deny that the space magic aspect feels more Star Wars than I can say I like in Star Trek.

So, what are your thoughts?