Hi,
Technically it could be possible as the first step of the E-6 process (first developer) is a phenidone type B&W developer which forms a silver negative of each layer of the film. Subsequently theres a water stop bath, a reversal bath and then a colour developer which forms dyes in each layer from colour couplers. This leaves a black and white image on top of a colour one, the B&W is then bleached away to leave the colour and fixed. You can do the same with C-41 films as the two processes are extremely similar with (hence why you can cross process them) but the C-41 process lacks the reversal bath.
All that you would need to do is only do the first (1st dev) and second step (stop wash) and then the fixing to get a negative B&W image, essentially the same as normal B&W processing. All colour processes involve creating a B&W image and then bleaching it away when the colour image is formed hence why you can 'bleach bypass' negative film (it doesn't work with E-6 though as your left with a negative on top of a positive) where the bleach step is skipped or reduced leaving the B&W layer, creating deep blacks and contrast with desaturated colours.