I can't access my vault (just like everyone and their mother) and I've got people in the wasteland. They'll probably be dead for weeks before the issue gets fixed, so will their corpses still be there?

I had this happen but because I just didn't play for a while rather than a technical issue. They were still there dead in the wasteland a few weeks later. (Of course, this was before Mr Handys collected the resources, so all my vault dwellers were dead from lack of everything, too.)