Correct FFF, your FAA licence will be restricted to the entitlements on your JAA licence, therefore to fly at night you will need to add it to your JAA licence. I have added the FAA IR to my FAA licence (which by the way dont forget entitles you to fly IMC on your JAA licence or even add the ticket if you so wish!), with no problem.
If you eventually decided you wanted to do the FAA CPL on passing it would then become a standalone licence and would no longer be dependant on your JAA licence being valid...