I was just checking out the "invisibility" wiki page after all the discussion. It just seems like a random set of abilities can be dodged with invisibility, and the others can't. Even similarly functioning bounces/abilities have no bearing on which way an ability goes.
Mystic snake can't be dodged, but paralyzing cask can be. Unstable concoction can't be dodged, but storm hammer can be. Concussive shot can't be dodged, but Heat-seeking missile can be.
I'd be hard pressed to find another mechanic more inconsistent. Damnit Icefrog!
For the ones that hit: "The following abilities assume that the target is visible when cast..." and I want to say it works the same for Heat-Seeking Missile. If you're visible when it's cast, and it's targeting you, going invis will not stop the damage. I don't particularly remember though.