It is my considered opinion that, because wearing the ring puts the wearer into some "other" zone, the cock/strap-on wearing rogerer's appendage would NOT disappear. *UNLESS* they were wearing a Ring of Power themselves (dwarf ring, maybe?) which would put them in, or close to, the SAME zone, although they themselves were not invisible. Indeed, is the One Ring wearer invisible to a Ring of Power (elf/dwarf) wearer? The One Ring wearer doesn't seem to be invisble to the Nazgul, who are wearing Rings of Power.

Also, the rogerer might experience some very disturbing sensations indeed. But or minds probably think alike on this one.