Air Conditioner - Grounding the Wall Sleeve

Does the wall sleeve in a built-in air conditioner need to be grounded?

Yes, the case is grounded. If the air conditioner is installed properly and is plugged into a properly grounded 3-prong outlet, no special precautions are needed to ground the air conditioner.

The left rail has a scratch pad on the front. As the unit slides into the wall sleeve, it makes contact with the metal base pan.  The sleeve is grounded through the base pan, which is electrically is connected to the power cord.  When the unit is plugged into a grounded outlet, the wall sleeve is grounded.