I only tried this once, and I was not doing it to test throw, but rather the cue ball had some crud embeded on it, so I had to have it cleaned... So this is not scientific. Also, the racked balls were not as unclean as you are discussing, these were probably used for only a few days before my "test". They were definitely dirty by my standards; they were visibly dirty.
The clean cue on dirty balls only reduced throw by a little bit in most circumstances in my experiment; once I adapted by adding a little more english, I didn't even notice the difference in most cases. Where the reduction was mostly noticable was when I was cutting a ball thin and trying to throw it to the max. In this case I lost about a third of the throw I had. But when hitting the object ball between half and full, I didn't really notice a big difference, I still had the ability to put more throw on the ball than most would consider reasonable.
Of course, that was one situation, your milage may vary. It's also non-smoking out here in California, so I'd guess it would be different if the balls are all covered in tar, like in some of the Vegas halls... Blech! Maybe the film of tar would make the difference even more slight.
