As you don't have a stand-alone FAA PPL, the short answer to your question is yes. In order to add an IR to your 61.75 piggyback FAA licence, you need to meet all the aeronautical requirements for the issue of an IR (61.65 of the FAR) and you also need to meet all the aeronautical requirements for the issue of an FAA PPL (61.109 of the FAR).
As the issue of an FAA PPL requires that you have completed 10 take offs and landings at night and a night cross country, you must complete these in order to then be eligible to add the IR to your licence. To be able to do these night flights you will require a night qualification on your JAA licence.
However, my advice would be to take some time to first get a stand-alone FAA PPL prior to doing the IR. If you already meet all the requirements other than the night flights, this really shouldn't take you too long and will be much better in the long run.
Regards,
HF