Yep, that's it. The Hawk was a naked bike. Any fairings were aftermarket and some I believe made the Hawk look a lot like an RC30. Once people picked up on the RC31 designation, they started advertising that fact on their bike too.
I think Two Brothers made a lot of aftermarket pieces for the Hawk.
Lots of guys I rode with back in the day rode them and raved about them, including a famous sportscar driver friend of mine. A friend of mine still has one and I rode it last year. Not much in the power or suspension department, but I'm comparing it to modern sportbikes. Even so, it was FUN to ride!
Watch your local paper or local motorcycle sales papers and you could probably pick one up cheap. I would only use ebay as a last resort.
--xTalon