Other than both using a pentatonic scale.. there might be something to this.
I've noticed, for instance, a lot of similarities in chords and progression in bluegrass and Chinese music. Others have noticed the same between Nepalese music and bluegrass (look it up on Youtube). Bluegrass is a giant mix of African and Celtic music, both of which make use of the pentatonic scale.
Thus, it's entirely possible. If Chinese people moved into the Appalachians by the 19th century, and stuck around, maybe something would've come up.