Almost on. Given that the RGB image is likely not tagged with colorspace information, the colors represented are a direct byproduct of the primaries of whateve

Almost on. Given that the RGB image is likely not tagged with colorspace information, the colors represented are a direct byproduct of the primaries of whatever display you view them on. That is, if your display happened to have the original CIE RGB color primaries, the 3D volume of colors would cover a greater volume. Of course, this too ignores the "stepping" between colors (bit depth) and also ignores the wider luminance gamut that a standard observer is capable of seeing. So the slightly more accurate answer to the original question is "Depends on what the primaries are of your display. Typically this is roughly sRGB, but if you are on a wide gamut display or projector, it will be larger."