no, the dye WOULD weaken it a little
ok.. in lacrosse, some people dye their plastic lacrosse heads... http://www.e-lacrosse.com/stech9.html
if you follow the same directions (give or take a few steps) you will dye it without any problems make sure that once you take the wheel out of the dye, you MUST rinse your wheel off, dry it, and then lay it FLAT ON ITS SIDE in the freezer. if you do not do this, the urethane will stay soft and break really easily. if you do not place it flat on its side, it can become slightly mis-shapen
hope that helps