You do not need a JAA NQ to add a FAA IR to your FAA PPL based on a JAR PPL. You do need one to fly a N-reg aircraft at night on your FAA PPL based on your JAR PPL:
I divided the regulations into two sections to clarify:
1: applying for the rating
2: the privileges of the license issued afterwards.
Firstly: you can add an IR to your FAA PPL based on your JAA PPL by meeting all requirements of FAR 61.65 or by complying with FAR 61.75(d) if you already hold an ICAO IR. If you were issued a FAA PPL without IR based on your UK PPL the FAA has concluded you met their requirements, right? This is where confusion starts, as the FAA issues the license and leaves it to the foreign pilot to know it's limitations (in this case no night flying allowed without JAA NQ) This is why Cusco needed to do his checkride during the day as acting PIC. When looked at again, different judgement is used (experiences as described by HighFlyer75 and Englishal) and the FAA PPL night time requirements are enforced before taking the IR. Cusco was able to avoid this somehow.
You do need a JAA NQ however if you want to fly at night in a N-reg aircraft when using the FAA PPL based on your JAA PPL. This is covered by FAR 61.75(e)(3): Is subject to the limitations and restrictions on the person's U.S. certificate and foreign pilot license when exercising the privileges of that U.S. pilot certificate in an aircraft of U.S. registry operating within or outside the United States;
When asked I always recommend people to get the full PPL, as this is only one of many disadvantages the "piggyback" has as already pointed out by Cusco.