It depends on what noise you are hearing.
If it's the sound of the door rollers going up and down the track or the rattling of the door panels or hinges, then no, this will not do you any good.
If it's the hum of the motor, then yes, a softer, less rigid suspension may reduce the amount of vibration that is transferred to the garage ceiling.

The noise is purely being transferred to the room above. Downstairs in the wall behind the garage I cannot even hear it opening. I realize it may be a waste of $32, but we'll see. I decided to buy these noise suppressing devices and see if the insulation they provide helps.

I don't know how your going to get much quieter than that. I have replaced my craftsman chain drives with liftmaster professional belt drives and the difference is huge.

If your rollers are metal you might opt for nylon rollers with real bearings which helps also.