Is moss a beneficial native plant?
There are many species of moss and some are native. Mosses have ecological and aesthetic values. They only thrive in areas that exhibit good air and water quality. Moss also acts as a great erosion control, helps retain moisture and nutrients in the soil, and adds a natural beauty to the landscape.
However, if moss is not growing in that location and is not growing elsewhere, this may not be a good location. You need a source, moist acidic soil, and shade.
You cannot walk on moss and it may have to be hand weeded.
Consider beds of other groundcovers, too.
Many ferns also make good groundcovers, especially hay-scented fern. Tiarella, Canadian ginger, phlox stolonifera, iris reticulata, and Allegheny pachysandra (not Japanese pachysandra) all are sturdy and do beautifully. They will enjoy organic soil and watering as they get established.
Here is more information on moss, lawn alternatives, and sources. http://extension.umd.edu/hgic/topics/moss-your-landscape