No. As per O.Reg 215/01 (http://hvactechgroup.com/files/regs/21501.doc), Section 20, a G1 certificate holder can,
Quote7. Install, repair, service and maintain electrical wiring from an existing branch circuit containing overcurrent protection to appliances in order to exchange, service, repair or install an approved appliance and carry out the replacement of electrical wiring necessary to complete the reconnection or installation of controls, control systems, components and accessories that are essential to the operation of the appliance, but the person shall not run wiring back to the electrical supply panel or perform any additional wiring unless he or she is also the holder of a valid certificate of qualification as an electrician issued under the Trades Qualification and Apprenticeship Act.
A 313A or 313D certificate holder can, but an electrical permit is required.