According to the owner's manual, no.
There are, however, serial numbers for the chassis and the engine that are cast or stamped into the metal... but they're different, at least on mine. Perhaps it would be possible to cross-reference those SNs through the factory? Otherwise, I'd try to find the original sales info, perhaps through the dealer -- if they're still around, that is. Or maybe the factory has records of units sold? (I should think they would.)
Engine model number and SN are cast or stamped, respectively, "on the right side of engine block, below injection pump." Chassis number is "stamped on right side of front frame" -- looks to be behind the right front tire. Hope this helps.