I'm not sure what is meant by "white gospel" or "falsetto" but there is a lot of what I call falsetto in white bluegrass gospel, especially in the early stuff. I took out a collection of Flatt & Scruggs (1948-1959) and the first cut of the first CD was "God Loves His Children" with Mac Wiseman (according to the liner notes) singing falsetto above Lester Flatt. It is most definitely not a high mountain tenor, although it probably doesn't qualify as white gospel.

Ralph Stanley often seems to go up from the high mountain tenor to falsetto. John Duffy sang very high, but it never seemed to be falsetto to my ear.