I don't see why QT can't support this. Swift and Objective-C objects map 1:1. Objective-C objects are just blobs of memory to other C-like languages. You'll be able to wrap all method calls with C wrappers.
Will it be easy? No. But it won't be any harder than it was with Objective-C. It's always hard to wrap an object framework with a foreign language.
As for Metro, I'd imagine it would be possible IF Microsoft allowed you to run non-Metro programs from their app store. I know nothing about it, but I suspect they might not. Would it be easy to wrap Metro? No, pretty hard. But it doesn't sound impossible. If there's a C interface, use that. If not, you feed method calls to the Metro engine as text strings.