Additionally, the ring doesn't have the 'power of Invisibility'. The ring contains Sauron's power, which is of the unseen world. Creatures who do not exist in this realm, are pulled there, and appear to disappear from the physical world when wearing the ring. This 'world' is more like a spiritual layer on our world.

If a creature who exists in both the Seen and Unseen wears the ring, nothing remarkable would seem to happen. So I believe if Elves wear the one ring, they wouldn't turn invisible. Perhaps even the three rings they wear would turn a mortal invisible by placing them in the unseen world as the one ring does.

Sauron of course exists in both realms, so wearing the ring doesn't switch him from Seen to Unseen like it does a Hobbit. And then as you say Chaladan, he just doesn't have the strength to manifest a physical body without the ring any longer.