Well, first off, love the name, though my favorite drow wants to stab you.
Now, about your post, there's some things to consider, outside of 'how will we get through security without a hacker'.
1. Any centralized school for magic-users, especially one that is cross-traditional, is going to be up to its eyeballs in megacorps. They might be funding it, or they might be the ones that actively put it together, or they could simply be keeping the school as a prime poaching ground for getting magical assets.
2. Remember the demographics, here. Awakened are roughly 1% of the population. That includes your high-level mages, but it also includes every barely-there almost mundane that has a single magic trick they can do, or are even only latent awakenings. Your population of people that have any talent worth mentioning is probably more around .01% of the population or less, and that's across all age groups. The number of teenagers showing the Talent, and strong enough to warrant training, is going to be smaller still. The number of those who aren't snapped up by existing megacorp recruiters (who are ALWAYS looking for more magical talent) is reduced even further, and concentrated primarily on the SINless, who also don't have money for training, as a rule.
3. An all-mage/adept team could work, though the lack of Matrix skills will hurt you, bad. The school aspect is the most problematic part of your idea, from a lore standpoint. Would work better as a wizgang, or as just a standard runner team that happens to be all awakened.