It's certainly an interesting idea; I would say a Hextech-themed support is long overdue, but I would make just a few suggestions that might (or might not) balance her kit a bit.
First, the idea of Material collection functioning as something akin to Thresh's Souls is interesting. The main problem I can foresee happening with a collectible resource though would be what happens when she runs out of it and is trapped under tower, unable to collect more, or during fights out of lane, such as at Baron or Dragon, where there won't be minions dying to generate it. I would personally say to treat Material as a currency more like Gangplank's Silver Serpents which would allow her to buy her personal items, and simply use mana for her abilities as that would prevent the aforementioned scenarios in which she might struggle to be stay effective (especially since she may not want to use her ultimate in every skirmish near Dragon or the like because, while having to use her ultimate carefully would help balance her, as enemies could disengage once they knew she'd cast it and the reengage after, I think Riot strives to never have any moments where a champion can't do anything at all). I would also say that instead of full fledged items, it might be better to have her buy augmentations (obviously under some other name, so as not to step on Viktor's toes, but for the sake of clarity, I'll continue to refer to them as such) such as +10% Bonus AP from items or +20% Base Mana-Regen (not actually balanced numbers, just place holders for proof of concept). That system could still be tricky to balance, but I think if it was made so that it would take a while for her to scale-up it would be okay, or if the augmentations had varying prices and so there was the trade off of 'Do I get the smaller buffs early or save up for one of the bigger ones?' could also work, but I digress and I'm getting a bit of a ways away from your original concept, but I just like the general idea so much it really got me thinking. In general, I would also steer clear of Material collection and the like affecting her abilities, because then it might feel just a little too much like Viktor.
On to the Q, I'd think it might be interesting to make it work so that the field would dissipate once activated if there were no enemy champions within it, but compensate for the fact by giving it a short arm time. In practice, it would allow enemies to quickly double back and escape, so those with fast reaction times could get out easily, but event of turret dives or similar events enemies could be face with the choice of 'Do I double back under the turret/towards the enemy or do I just take the slow and continue forward?' That might tread a bit close to the false choices Riot tries to avoid, but I think it might be okay since it wouldn't be hard CC.
As for the W, abilities that are passives are always a bit tricky, to make worthwhile leveling up, but I would say if we assume, for this purpose, that her Material is used to purchase augmentations, make the passive lower the cost of her augmentations by 5/10/15/20/25% (and perhaps call it something like 'Efficiency' or 'Hextech Innovation') so that she would again be able to make the choice of 'Do I buy my bigger buffs sooner or do I improve my CC/other abilities first?' which would give her a lot of flexibility in terms of when she hit her power spike and reward players for correctly assessing the flow of a particular game. I also might throw in maybe some small other bonus like her auto-attacks do 1/2/3/4/5% of her AP as bonus damage so that she has an extra incentive to level the ability up and which would compensate not increasing the base damages on her other abilities.
In terms of the E, I'm not sure 'Corruption' really fits with the Hextech theme all that well. Yes, Hextech incorporates magic, but the idea of corrupting something fits a little better in with the lore of the Shadow Isles than Piltover or even Zaun really. Damage amplification is also tricky to balance, as I can see enemies just getting tagged with her ability, and then blow up incredibly fast by a LeBlanc or an Ahri. I'd think that Armor Shred might be better as, if she's a Support is will synergize well with and ADC, but avoid the 'Now everyone on their team can blow me up' problem that might arise with damage amplification. Something along the lines of being armor-piercing or acidic would also be a bit closer to Hextech thematically.
The Ultimate I would say is pretty good where it is, especially the Cooldown Reduction allowing her to really be a CC bot when she activated it, but I might include something about temporarily buffing the augmentations she's purchased, then giving the ability a long Cooldown (maybe in the two-minute plus region) so that it likely wouldn't be available for every fight or skirmish, but the enemy team would really have reason to be afraid of it when it was active. It would also culminate in making her scarier and scarier as the game went on, which would be interesting for a Support to actually become a potential threat of some kind, with the trade off being she'd have less to offer than most in the early and mid game than some other Supports.
I really liked your idea and I'm terribly sorry if I hijacked it a tiny, but I've been thinking about how to make Hextech Support of some kind recently and so what you wrote just kind of resonated with some of the ideas I've had floating around already. Obviously you take my suggestions with a grain of salt, but I just wanted to make them. One last thing being maybe go with Zell(e) or Xell(e) over Nell, just because while the melodiousness of the 'ell(e)' work well for a Support, most of the Hextech champions tend to use some harder sounds or more unusual letters (Vi, Viktor, Jinx, etc.) and so it be a bit more fitting to blend the 'ell(e)' with something like that. That's just my two-cents though, and I just wanted to say again that I love the idea and thank you for sharing it! ^_^
