Multi-player wouldn't work unless they disabled VATS while in MP.
Well, they could make it work in one of three ways:
1) it stops time for both players. Too bad so sad.
Maybe have a 10 second timeout and then you cant use it again for 10 seconds.
2) it doesnt stop time at all, so you'll need to select targets at range or REALLY quickly.
3) have hotkey targets set up when in multiplayer. Basically you could set up macros for "1 vats head shot" or "max vats torso shots" and just click the button, but it plays in real time. No stopping or no slowdown.
But yeah. It would kind of svck.
There is always that fallout-like MMO called Fallen Earth. I never tried it, but hey. It might tickle your multiplayer apocalypse itch.