The ice melts. Rapidly. It is possible to use ice if you have an open tank. However, everytime you add ice... you dilute your dye. If you don't want to dilute your die, you would have to have a secondary water system!
A secondary could be as simple as putting your radiator/heatercore into a bucket of water to which you add ice. Often. Or, you could have a pump which circulates icewater to somehow cool your primary water loop.
In any case, I don't suggest it. It's much too complicated, and you'd be trucking up ice every 15-30 minutes. If you ever stopped adding ice... system failure. I used it as a temporary measure when I discovered my radiator was too wimpy for the heat load, but I quickly switched back to air cooling. That is how much of a pain in the rear it is. I wasn't using dye though.
The YY cube looks nice.
Have fun!