The visible light spectrometer will "see" the mixture of pigments exactly as would your eye: less absorption in the green region, and more in the blue and red extremities. Pigments appear colourful because they
subtract from the colour components of white light, so it's helpful to imagine starting off with pure white light made up of all the colours of the rainbow.
A bright lime yellow pigment will absorb poorly in the yellow and green region of white light. All the other colour components (red, orange, blue, violet) are properly absorbed and hence subtracted from the white light.
Similarly, the blue pigment may absorb poorly in, say, the green and blue region, while it subtracts red, orange, yellow, and violet.
When the two pigments are mixed, the mixture will absorb (subtract) red, orange, yellow, blue and violet from the full spectrum white light, while absorbing only poorly in the green region. Visually (and spectrophotometrically) we see a dull green.

Some pure pigments (such as the phthalocyanine greens) are inherently, well, green. They can give brighter shades of green than a mixture of primaries.
Rigil