Rain will both erode the topsoil and leech away nutrients. For long term storage, compacting the top layer of the pile will help against erosion, though the use of a tarp is still recommended.

Should you ground cover mulch?

Yes, I recommend using mulch the first season when establishing a groundcover. It will help to suppress the weeds while the ground cover fills in. If it is a groundcover that spreads by stolons or above-ground stems, then I would go a bit lighter on the layer of mulch.

Does rain ruin mulch?

Rain makes mulch twice as heavy, which in turn makes me twice as tired, twice as sore, and a few pounds heavier from water-soaked clothes. Wet mulch also sticks, making it harder to spread and harder to clean off of the driveway in the end.