Oh, I don't think so. Like a lot of summer annual weeds, red root pigweed starts from seed in the spring, grows, makes seed to establish the next generation of pigweed, and then gets killed at the first frost. Waiting until the beans turn brown is like shooting a terminal cancer patient days before the natural end. At the point you propose spraying, next year's seeds are probably already on the ground. Even if they aren't simply killing the plant accomplishes nothing (am I wrong?).
The whole premise of weed control is to get the bad plants when they are small, before they can establish competition for water and soil nutrients. Dead early, no seeds -- although they will come from somewhere else.