Eddie Lawson raced a KR250 at Daytona (and even a KR500), cant recall if it happened more than once, but the bike certainly made it to the USA too.
The bike i linked to is a PEM framed KZ1000, from the early eighties, an offcial works kawasaki france endurance bike.
Not an expert on big Kaws but its certainly air-cooled , looks to me like the late, so called J motor...
The "Formula 1" class of late 70's-early 80's in the USA allowed pretty much anything with a motor and two wheels, problem with it was the dominance of the TZ750's, they didnt leave too much chance to anything four stroke.