Yes, that includes the wheels, handles, and any bulges on a soft bag. Be careful. The measurements provided by the luggage manufacturers do not usually include the wheels or handles. Carry a tape measure when you buy new luggage and measure from the top of the handle to the floor to get the height measurement and if the bag has a side handle, be sure to include that in the width measurement. That 62" measurement is height + width + length, including all wheels, handles, and any bulges. Airlines want to make as much money as they can on luggage fees, so the employee who is measuring is not going to be measuring in your favor.
I once saw an Air Tran employee measuring a duffel that would not stand up on it's own. She leaned it against the edge of the scale and when she measured the width, she measured from the edge of the wall to the edge of the bag, including the couple of inches of open space between the wall and where the bottom of the bag started in her measurements.