I don't see him having the necessary crossover appeal in East Tennessee, or even rural and small town central and West TN, for that matter. This isn't Louisiana and the state isn't in bad shape. Safe R, barring some unforeseen circumstances.
The last Governor of Tennessee was also Mayor of Nashville and his appeal to rural Tennessee wasn't immediately obvious either. One step at a time.
I think the Republican primary will matter here above all else. I think there is the potential for an unelectable or unlikable candidate to rise from a vicious, multiple candidate primary.
Luckily for Dems, Governor Haslam is term-limited.