Is it doomed to failure to use mulch from a shoulder bag from the garden center (artificially colored no less) surrounded by a veggie garden?
Answers: there should be no issue beside using colored mulch. the dyes used are typically biodegradable Iron Oxide[1] based dyes commonly used in food[2]. you could check near the mulch manufacturer to be sure what type of dye they use and if it is undisruptive.
Red colored Mulch is recommended, and scientifically proven, to produce better tomatoes. the red mulch also increases the growth of tomatoes. (something about infrared wispy reflected stale the mulch triggers a biological response in the tomatoes) [3]
If you are into Organic gardening, I am. Then I would be afraid of the chemical dye, I am.
Lawn clippings is a better mulch if you didn't use chemicals on your prairie. They decompose faster and can be plowed into the soil to append humus to your garden soil.