AR-Es1 grounding

I have a AR ES-1 turntable with a two wire power cord. Could I install a three wire cord and ground the tonearm and motor to the power plug grounding wire? 
Yes, but don’t.

The power cord’s ground is not for noise, it is for safety. It is designed to keep the metal chassis of a device at ground. If there is an internal short to the chassis, instead of you dying from electrocution, the ground forced the fuse to blow.  Clearly, this doesn't matter for wooden chassis components. :) So unless you have a safety issue you are concerned about, leave it alone.

Any more grounding of the turntable and you invite a ground loop.