Rats. The [none] (no-color) swatch is stubborn.
I was able to remove the [registration] swatch from the mix by making sure it's at the head of the palette and adding a (If swatchIndex>1) test to the script. But I can't get rid of the [none] swatch no matter what I do. Illustrator must treat it as a special case so that it cannot be referred to by index number.
Help, James!
One other thing: Not for nothing, but...
| lets say I have 600 different objects in illustrator (just little circles with a fill color, no stroke) and 6 different colors that these circles should be. That means, I'd like about a 100 to be one color, 100 another color, etc. |
...is not exactly the same thing as...
| select all 600 and just tell Illustrator that I have these 6 colors and I want to apply them to the selected objects randomly |
What you want is a uniform distribution of those six colors but in no discernible pattern. That's not true random assignment, and this script won't get you there even if got the unwanted swatches out of the mix.
No obvious solution here.
OK. Got it. Had to modify the script a bit more.

As I wrote in the previous post, this is done with a random number generator, and that's not exactly what you want. But if you want to play with the script, here is the modified version:
http://harron.home.acedsl.com/Misc/HKA_RandomSwatchFIll.zip
Make sure you make the undeletable swatches -- [none] and [registration] -- the first two in the palette/panel.