No, it cannot be run in 650 class. Same for the BSA A65, which is 654cc. You can sleeve it or de-stroke it. De-stroke may be possible by getting the crank ground down offset to the short side that is, 53.5mm stroke to get 645.7cc, if undersize bearings are available.
From the BMST rulebook, "1. Production (P)
a. Use the same engines (gasoline only) originally
installed in the specific motorcycle frame at the time
of production and ensure it meets the definition set in
the ?P? frame class (See 3.11D). Original equipment
(OEM) shall include cylinders, cases (crankcases),
heads, and carburation or throttle body (stock venturi
size), kick-starter or electric starter. Displacement
determines the class. OEM displacement specifications
must remain stock."
I don't find any exception to displacement for any other classes except Vintage, which allow .050" overbore to remain in class.
Although your question in under the BMST section, the SCTA has an interesting section as follows. SCTA (2017 rulebook) in rule 7.D.3 for classes other than Production allows overboring of cylinders by .020" (.508mm) beyond that which provides maximum displacement for the class if the OEM bore diameter is within .020" of the maximum displacement. As I read this, it would allow, for instance, a 650 Triumph to be bored out to 658cc and still run in the 650 class. But neither a 650 BSA (which is OEM 654) nor your Kawasaki 650, would be allowed to run in the 650 class even if on the stock bore.
Tom
