It is not a dumb question, but the answer is almost certainly not.
It wouldn't be that difficult to design a computer to process graphics a lot faster in greyscale (you need to use one byte for the color and one for the alpha) since each pixel requires less computation.
In practice if your graphic card only worked in greyscale, it wouldn't be worth the cost of development and so nobody would do it.
This might be the dumbest question but is there a system performance benefit in using grayscale?