That knock-off adapter will almost certainly only charge, not pass through music or any other signal to the device. The Apple adapter has a DAC in the actual adapter for just this purpose. Note that many of those reviews are for regular cables, not that adapter, and that many of the reviews for the adapter state that it won't play music.
FWIW, 30 seconds with a dremel tool will modify Apple's adapter cable to fit any case...
That is why I linked Apple's option. It is the second link. I'd rather buy another $30 cable than modify a $40 case (just my personal preference).
But... I have some knock-off adapters. (not from the specific site... eBay) And they do charge and play music.