Can a 240 volt circuit using number-12 wire handle a 4500 watt appliance?

No, the 20 amp (AWG #12) wire will be too small, you need to use AWG #10 wire. Even though 4500 watts is less that the 20 amp it can only be loaded to 80% by NEC rules which is 18.75 amps. The #12 wire would be overloaded so defiantly use AWG #10.