I tried to imagine Dolly Parton singing Vocalise. She undoubtedly has heard it, and could probably do a fine job with it. I’d guess most big-name singers were introduced to, and probably trained on, some of the classical composers. I suspect her fan base would be respectful, admire the result, and maybe even ask for it now and then.
How about the reverse? The themes are often similar. Consider Drinkin’ Problem vs Carmina Burana. And quite a few composers were inspired by folk tunes. For American tunes, think of Copland. I have to confess I’m not terribly fond of his work.
For apples to apples, and maybe some actual fusion works, you’d have to look at short pieces. Ballads can run on for a while, but I haven’t heard many that were musically complex, though some short country songs are. So "short" is mandatory. The most famous compositions by the big name classical and romantic composers are far longer than your average song, and generally quite complex, but they wrote plenty of shorter ones too, and modern songwriters borrow from sections of longer works. (a partial list) And besides tunes, country composers can borrow what melodic tools they please from the common heritage.
You shouldn't need a steel guitar or a fiddle to reproduce the country musical idioms.
I don’t see why this couldn’t work. Which probably means somebody did it 70 years ago and I never got the memo. I try to research posts, but there's a lot I don't know. I never got very far in music theory. There's probably some key word of jargon that would have made google tell me all.