Hmm. I'm actually kind of curious what a nuclear exchange scenario would look like. It would almost certainly be the United States doing the first strike - they've always been by far the most trigger happy of the great nuclear powers.
Maybe the US tries to nuke China after prolonged South China Sea saber rattling ends with China sinking an American ship, and then everything else cascades into a full exchange?
Sabrina would need to spend a long time picking off missiles already in flight with Homura's powers.
Believe it or not, I actually had an idea in mind for exactly this scenario. Sabrina would see mention of rising tensions on the tv, then she'd go about her day, then Mitakihara would get hit by a nuke (Sabrina may or may not have seen the nuke, though I imagine that by the time she'd be able to see it, it'd be too late.).
Also, your scenario earlier about Sabrina not being able to find most of the missiles seems rather likely. I don't see any real way for her to find and track every ICBM, especially considering most will have entered sub-orbital spaceflight at some point and that earth and it's atmosphere is a freaking huge place, even for an ICBM. plus, If they've already gotten to space, most ICBMs don't rely on propulsion at that point from what I recall, so it'd literally be trying to find a metal nipple in space. Not to mention the actual bombs from planes (though easier to spot, harder to get rid of without killing the men inside) and missiles from submarines.
I suppose ultimately it all depends on how quickly things escalate and how soon Sabrina is able to react. It is very possible that she won't be able to react at all, if she finds out too late about what's happening.
Also also, I'd imagine that Ionizing Radiation causes permanent damage to the soul gem, because in real minerals, radiation from inside the mineral actually causes damage over time (In fact, this is one way of telling the age of a rock, though not as reliably because moderate heat and pressure can 'fix' some of the damage, making the rock seem younger than it is)