Many times when doing burn parties on weapons, I've started a song, had Whirl of Rage go off (and gotten the stun icon), had the stun wear before I completed the cast, and had the song still go off.
Of course, it's entirely possible that the rules are
a) different for songs, or b) different for "physical" stun effects on songs, since there are already things that can interrupt a spell but not a song. Somewhat obviously, if I'm still stunned by the time it hits the completion percentage, the song does not go off. I'm not sure what would happen if someone/thing casted the spell Stun on me and the stun effect wore off before my song went off; so few things cast Stun on BRDs that I've really never had the opportunity to find out (I do not do Ballista).