Can I use a 6 pin Bluetooth module in a 4 pin socket?
After some more concerted searching I have found the answer on Success Using the JY-MCU (linvor) Bluetooth Module:


  The module has 6 pins labeled on the back, but most modules only have
  4 of those populated with pogo pins.  KEY &amp; STATE seem to be not
  required, as KEY is used for flashing the device and STATE simply
  indicates if the device is awake or not.  So that leaves only GND,
  VCC, TXD, RXD.  Not shown is Pin 11 which is the RESET pin, resetting
  the module when pulled LOW.


So, the answer is apparently yes, and you can buy a cheaper 6 pin module and remove (snip/desolder) the two additional pins.  The EN pin is also apparently labelled as KEY on some modules.