Hi Bo,
Diversity helps with a wireless issue known as "multipath". It's when the originating signal arrives multiple times at the destination.
http://en.wikipedia.org/wiki/Multipath_interference
Diversity is not required, but it is very noticeably helpful in factory environments, or any environment with a lot of metal or reflective surfaces in it.
As long as you are configured to use only the right/primary connector, the dormant left connector will not cause any problems for you. If you do install a diversity antenna, make sure to make it the exact same antenna that it connected to the right/primary, and also make sure that it covers the same space that the primary does. Place the antennas apart by the same distance that the connectors themselves are apart on the AP.
Jeff