A dye won't affect your pump. The only way it would, is if you used a soluble dye (i.e. a powder), and if you didn't dissolve it properly. Otherwise, for all practical purposes, it's a liquid (highly diluted in water).
Since you mention the res, then I have to guess that you're building a "pretty looking" system, with windows, right?
There's not really anyway to tell for sure if the dye will stain anything, just because there's too many factors. You just have to try it, and take some measures to prevent it.
The res shouldn't stain (guessing). If you suspect it might, then try spraying the inside with something like Pam (cooking oil spray), then rinse it out with water. This should fill any of the minuscule cracks with a water repellant substance. (Hey, it's just an idea!)
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