Is 'sind ohne Wasser' more idiomatic than 'haben kein Wasser'`?
sind ohne Wasser is just as idiotic [sic!] as haben kein Wasser. I don't think either sentence makes any sense.
Would : "These cups are empty" work? or is the mentioning of "water" important?
I'd like to know that too.
Not really, they could contain wine or anything else, strange phrases, yes... but still you shouldn't add a different meaning :)
Diese Tassen sind leer -- is fine.