I agree with DublinPilot. Legal wranglings aside, your FAA piggyback PPL will be restricted to private operations only, and whatever restrictions your original license limits you to.
As you are not limited to day VFR only by your original license (being the holder of an IR), you can fly VFR at night in the US. (After all an FAA PPL training course by default includes the night flying, so an FAA PPL by default has night privileges.) For IFR privileges you'd need to do that extra test.
Looking at the legal wranglings, Silvaire seems to suggest that your FAA piggyback PPL will not be restricted to day VFR only, if the JAA day VFR restriction is not written explicitly on your license, but is embedded in JAA/EASA legislation. That may well be true, but would it be wise to do night flying in the US without further training, when you've never had night training at home? Just because some civil servant wrote the word "on" when he intended to write "of"?
Furthermore,
So in the case of Victo my opinion is that he can only fly night in the US under IFR so on an IFR flightplan, albeit in VMC conditions.
This is just complicating matters to no end. It used to be the case in the UK that night flying was only allowed under IFR, but night IFR was possible for someone not holding an IR (just the NQ), although in VMC conditions only. The UK, thanks to EASA, is now in the process of changing over to what the rest of the world already knows and does. Night VFR is just that: Night VFR.
Trying to transpose this unique UK phenomenon over to the US will just confuse the hell out of everyone. Most likely ATC since they now will need to vector you around IMC areas, while you are listed as an IFR flight on your flight plan.