Robert, I don't know about Tom Dula's thinking, but you're quite right about Union sentiment in the mountains. (Barely related footnote: Confederate soldiers deserted in large number throughout the war, mainly to take care of their families; many returned.)

You'll have noticed that in the DT version, the singer is explicitly a Unionist. In the original attributed to M. B. Smith - and usually collected with few changes besides the inevitable memory lapses, the singer's loyalties are unmentioned - and indiscernible - which is part of the song's greatness.

There were Union people all over the South, not just in the mountains and Mississippi's "Free State of Jones." Some joined Union regiments if they could, most just kept their mouths shut. You'll recall the lines in Henry Clay Work's "Marching Through Georgia" (1865):

"Yes, and there were Union men who wept with joyful tears,
When they saw the honor'd flag they had not seen for years;
Hardly could they be restrained from breaking forth in cheers,
    While we were marching through Georgia."