Well, let me say first of all that I am not a bass builder, nor have I personally experimented with this, but I have had quite a few discussions about it over the years with some instrument builders, as well as lively discussion online.
With string tension at the nut, there are two forces: Tension pulling the string away from the bridge, and tension pulling the string against the nut.
Tension pulling away from the bridge determines the pitch, so assuming that the string stays the same and the pitch stays the same, the tension pulling away from the bridge must stay the same.
Tension pushing down on the nut is important for the open strings. Once you fret down on a note, the vibration of the string goes from the bridge to the fret you are pressing down. The string from the tuning key to the back of the fret is taken out of the equation.
If tension against the nut behind the fretted note had an affect, than it also makes sense that pushing down on the string behind the fretted note, but still on the fretboard, would also have a similar effect, although maybe not to the same degree (for example, if you were playing the 4th fret, holding down the string on the first fret would also put more pressure on the nut). Unfortunately, that would also slightly change the intonation, so that may not be an option for real life playing.
I guess an easy way to test this would just be to record the bass with the string through the retainer, then record it with the string outside of the retainer. I mean, for the heck of it, you could pull the string off of the nut altogether, put some foam down over the nut, and have the string pushing on the foam. It would obviously keep you from playing the open notes, but I would bet that the fretted notes sound exactly the same.
If this is wrong, I would love to have someone explain why, although over the last few years I have yet to hear a real scientific explanation as to why the retainer may improve the sound.