Rather not. The other way around (i.e. unnecessarily running the thingy with a step-up, if it's already in 110 V configuration anyway) would be dangerous - whereas if it's in 220 V configuration and fed with 110 V, the motor would see an even lower operation voltage due to the drop-down resistor in series, and I don't really see, how that could fry the motor...
Well, and regarding the adaptor, maybe the owner at that time simply wanted to keep the unit as original as possible - and those simple adaptors aren't exactly expensive, either. Or that owner deemed it possible, that he might move to a region with 220 V mains voltage again sooner or later...
Greetings from Munich!
Manfred / lini
Synchronous motors run hot on low voltage. They draw more current, and "slip" more trying to maintain speed. Both generate heat. In 220v config, this thing has a resistor in series with the motor. In 110v, power is applied directly to the motor. At the very least, it would cause the motor to struggle to maintain speed if it's not wired properly. I wouldn't trust it at this point.