Yes, indeed, you can get very good B&W negatives from C41 negative film.
I take B&W print developer and dilute it. Say you use Dektol. Instead of mixing the stock solution 1 + 2, as is usually the case for prints, dilute that stock solution 1 + 19. Then, depending upon the temp you wish to employ, time your development anywhere from 6 minutes (85F) to about 12 to 15 minutes (low 70s Fahr). Find a time and temp most suitable. You will get a rather dense negative, maybe one where it is difficult to see the image. (Do not judge image quality until after reduction. After fixing, rinse briefly.
After full fixation, place in reducer. I use 3g of potassium ferricyanide in water to make 200mL. To this solution add about 40mL of new paper-strength fixer.) This solution keeps for maybe 30 minutes so mix it up just before use.
When reducing, make certain to keep agitation consistent so as to reduce evenly. (Don't reduce the whole roll at one time: See below.) With fixers, it does not matter if some parts of the film fix faster, because you fix to completion. But with reduction, this is not the case and you must stop reducing at the proper time. It is best to cut off a few frames and place them into a tray so you can observe and stop that procedure quickly. After a few minutes you will begin to see the film base start to become brighter and brighter orange. This is your clue that the reduction time is nearing completion. You will also see an INCREASE in both contrast and image density manifest. It is imperative that you do not go too far or you will have no, or little, image left. Done properly, you will have a magnificent image that has full contrast and sharpness with little grain. (You might wish to further dilute the reducer with water in order to augment the reduction time.)
Because of the quickness of this procedure, you are best advised to give one stop more exposure so that shadow detail does not get wiped out with the reduction. It takes a bit of practice and you are foolish if you attempt this 'after fixation' reduction process with a full roll of film. Again, this reduction imparts an increase in image contrast that is very pleasing to print; in fact, the contrast you will attain might be deemed by you to be excessive, but I state this because with an orange mask, your negative will automatically be 'seen' as having a grade one filter by most VC papers. (If you use graded papers, give less development time to the C41 negative.)
After fixing, cut off a few frames and do what I said to do. You will be amazed and, as a bonus, you will have full cloud detail without use of a filter because color film captures all the hues. It is important to reduce until the base is a bright orange or else you will have grain problems and a 'dirty' negative. - David Lyga