That would not make any sense to me. However, I garden for the birds, insects, critters, and lastly, humans, so I cannot imagine using glue of any kind to hold mulch in place. I know I sound like a curmugeon, but I don't mind sweeping when it is needed (very zen) and love seeing the birds, especially the robins, root around looking for insects and worms which they need now to feed their young as well as themselves.

If the mulch doesn't stay in place, replace it with a groundcover. I can't imagine that any glue that will last and be effective won't essentially turn your mulch into something strange or any glue that keeps the mulch natural would be effective.