Can I use Sphagnum Moss as a ground cover for my Chinese Elm Bonsai to keep the moisture in?

I guess you can. But the real question is if you want all the roots to grow to the top of your soil for water or to the bottom.

You can, but honestly I only see people doing that when trees where just repoted, or when nurseries send plants by deliverer/packaging, so you receive it hydrated.

I would only advise you to be carefull, hiding the substrate can trick your watering management...

Covering the top of the substrate does keep it moist longer. It is especially usuefull to get suface roots.
If you need it to avoid drying out beteen watering, it would be good to look into overall care.