As for "Luohan" being pronounced "Lohai" or "Rohai" in uchinachu, that might be a possibility, however, one simply looks at the kanji as the ultimate source.

Personally, to think there is one Chinese source for kata, I do not think so. The Okinawans were able to get a good understanding of essential quan fa and make up their own inspired kata. Okinawan kata are made up and took a smattering of Fujian based Quan Fa and combined it with their native "Di" or "Te". They weren't Chinese and didn't have to have all the Chinese baggage of mastering an art with all the requirements passed down.

As for Luohan Quan, there are hundreds of fist forms referred to as "Luohan Quan".

A look at Rohai, and you know its Shuri Te or Tomari Te...not LuoHan Quan. Pinan Godan, Passai look more like Luohan Quan, even the Jion, Jitte, Jiin kata.
Robert Chu