Answer: According to information supplied by the manufacturer, Round-Up is both a contact herbicide and one that translocates to the roots of the plant to kill it completely so there's no resprout. The product is not supposed to leach into the soil and it biodegrades rapidly in sunlight and air.
I think your question was more of a safety issue than one of effectiveness of the product. Since you're going to till or dig your veggie garden anyway to add organic matter so your veggies will thrive, why not just dig out the weeds, roots and all, and apply a thick mulch over the surface of the soil to suppress weeds and keep weed seeds from germinating? This way you'll be adding good stuff in the form of organic matter, and you'll be keeping potent chemicals out of your food garden.
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