No, there was never a specific game dealing with the Orange Island series. That whole story arc was kind of a throwaway thing, anyway, and it was only really made because there was some extra time between the completion of the Indigo League and the release of G/S.
The Orange League really is sort of useless. The story arc never was finished. The great mysterious GS Ball around which that entire season was based was only half heartedly brought into the next season. In fact, the GS Ball that everyone was so excitedly talking about for 30-40 episodes was simply dropped off by Ash and never heard from again. (The writers had no idea what to do with it, and they were hoping fans would forget about it.) The only thing that survived the series was the idea of double battles, which would go on to become an interesting addition to the Pokemon games.
The closest thing to the Orange Islands in the games is in Firered and Leafgreen. There are seven islands to explore located in the ocean to the south, and it's generally understood that these were inspired by the Orange Islands.
This all being said, the Orange Islands are still somewhat fun to watch, as they were created before the Pokemon anime series completely degenerated into the pathetically formulaic slop that it is today.