You know, it could work. They would have to put a LOOOOOT of effort into it for it to work, but they could.
The first step would to have it be a completely normal overworld and command set-up, keep the unique part of X-COM going. But then, aliens strike! You go into the set-up, fly out, whatever, and get a sort of Ghost Recon/ArmA 3 esque overview of the area you will be fighting in. Choose a landing spot (preferably a LOT further out, so you have to actually advance into the AO) and send your team in.
From there, you can control them in real-time from the above screen, but if you select one you jump down into FPS mode. This would be a very realistic, very ArmA 2/3 or SWAT 4 style gunplay and gameplay. Moving carefully, calling people up to advance and cover. When contact is made with the aliens, panic sets in. Most units should have some sort of panic meter that affects their aiming and eventually causes them to duck and cry in terror. The same system could be applied for suppression, on both you and the aliens.
The key point of all this is if you get hit once, maybe twice (at least at the start with basic armour), your soldier suddenly bites the dirt and you are thrown back to the overview or into another soldiers eyes. Ambushes would be terrifying as you are wrenched into another soldier's eyes to see your headless corpse flop dead in-front of you.
More elements would have to be put in to really make it shine, like heavier helmets restricting your view, but maybe upgrades giving you in-helmet displays like radar and squad status. So sure, you can all go in heavy armour, but expect to panic when you are tunnel-visioned and Chrysalids are rushing out of the darkness at you. VR would be very cool to see in something like that, but they would have to include a head-turn system at least.
Very important would be a restriction of ammo so you can't just blast everything, as a dead mans trigger in a combat like that is not want you want to hear. Having very, very tight controls for the AI when they are not under your control is important, so telling them to fall back and find cover or to push and advance in different situations is essential to not have players rage when everyone is gunned down because they took cover against the sectiod, not the twenty-good-thin-men.
Lastly, and I'm unsure of this, maybe you could have a pause mode when you jump back to overall command. The only reason I say maybe is because I feel it might detract from sudden ambushes and such where your reaction time is key to surviving.
So yeah. It could work. I may have given it too much thought. But the key part is that they would have to go the full way, whole hog, etc., because any half-hearted attempt will result in the biggest shit-storm since the announcement for the X-Com Pachinko machine (note: this does not exist. I hope.)
EDIT: As someone mentioned, the Brothers-in-Arms games would be a good guide as well. Squad based suppression and flanking was fucking awesome in those games, it would be pretty cool to see that in this. EDIT: Also, I could see this being a MAJOR hit with the ArmA 3 clans, and other realism gamers or just general hardcore mil-sim fans. Imagine if each battle could have soldiers controlled by other players with someone running commander. That would be intense as all hell, and I would pay faaaaar too much to play that.