Mounting a speaker this way has absolutely NO effect on the output of the system. Doing this does not make the sub any louder or quieter. Inverting a sub does however change the volume of the box, sine you're moving the mass of the driver's motor structure outside of the enclosure, effectively increasing the net air space inside the enclosure.
This can alter the response of the box, or change the tuned frequency of any ports.
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[/CENTER]So, to answer this commonly asked question, no inverting a speaker doesn't affect the output in any significant way. It's mainly done for looks and bling factor.