After a decade of using a microwave oven in my house I figured out I never cared to connect the grounding cable. So my question is regardless of electrical shock risk, does the Microwave Faraday cage shielding work without a ground connection? I am afraid the shielding require a ground connection to work and hence a lot of microwave radiation leaked. Is that correct?
The grounding cable is to prevent a surge in current from producing a shock danger at the case of the appliance. It has nothing to do with the Faraday shielding. Metal absorbs microwave radiation whether in an electrical appliance or not, and even the glass window is an effective Faraday shield because it has embedded within it a wire grid whose holes are much smaller than the 'wavelength' of the microwaves, rendering it opaque to that frequency.