I don't know what you mean.
A B&W sensor, in my book, means a sensor without the Bayer filter array. If the current A12 were to be made without the color filter but it has everything else (ie., the offset microlenses and the UV/IR cut filter) then it will be capable of imaging in the spectral region of ~400 to 650nm (blue to red) just like a panchromatic B&W film covering the entire spectral region unlike an orthochromatic film.
Every black and white film, whether orthochromatic or panchromatic, has a signature sensitivity curve (records different colors of light differently) both built into its chemistry and affected by how it is processed. You adjust that sensitivity curve by filtering the light striking it with red, orange, yellow, green and blue filters in order to effect tonal separation of colors in the captured image. In the recorded image, there is no distinction as to whether the original subject reflected red, green or whatever color ... that is set, fixed by the recording medium. You cannot change it, only adjust the intensity.
With a color sensitive recording device, you have the information about the mix of red, green and blue at every point in the original scene. With that information, you can separate red from green, blue from yellow, and adjust those relationships in the rendered monochrome image.
A B&W sensor may be panchromatic, but you don't have any information in the captured data about what a particular color in the original was therefore you have no capability of manipulating tonal relationships based on original color after the fact. A color sensor allows you that dimension of control in your rendering process, and simplifies what you need to do (and carry) during the capture process.
This is the benefit of the evil Bayer array: it gives you rendering control, adds information into your captured data, where otherwise you have to make those adjustments yourself with filtration prior to capture.
I'd quite forgotten just how important this was in b&w film photography until I acquired the M4-2 in September and started shooting B&W film once more. I wondered why my images were all so flat looking ... and then I remembered: I used to always fit an orange or yellow filter for some subjects, a green or blue filter for others, a red filter for others. Once I started doing that, my results began to approach once more what I do with rendering monochrome from digital capture. It's a heck of a lot more work ...