Is it a good idea to connect the mounting connectors of a USB port?
Mechanical reasons, the more copper around connectors the better so if your worried about it ripping off of the board more copper will give you more leeway before it comes off the board. 

You will get half of the inductance if you connect both so if your worried about radiated emissions out to the cable or conducted emissions to your board (assuming you have one ground and not a shielded ground.) 

The shield is already tied in the case so the yellow trace is redundant.