The answer is YES:

The C-41 color developer is a typical (non-staining) black & white developer. Its job is to differentiate between exposed and non-exposed silver salts present on the film. The developer then goes to work on the exposed silver salts. They are reduced to their two component parts which are silver and an halogen (Iodine – chlorine – bromine). The halogen portion is dissolved by the waters of the developers. The silver portion is precipitated as an opaque tuft of metallic silver. The result is a negative image of the original vista.

The C-41 color developer also contains a color developer. Its job is to couple with incomplete dyes imbedded in the color film during manufacture. This action completes the dyes. Should this happen, the dyes blossom and become cyan, magenta or yellow dye globules, based on which emulsion layer they are in. Since a black & white film is void of these incomplete dyes, no such action will occur. The result will be a black & white negative.

In the C-41 process, the film emerges from the developer with three dye images, and three silver images. The silver is opaque and thus veils the dyes. The C-41 process contains silver bleach. Its job is to convert the silver image back to a silver salt.

Next the C-41 process fixes the film using a typical fix bath. IF the C-41 solutions are of an abridged type, the bleach and the fix step are combined making a bleach-fix or blix. The color film emerges, whereas the silver images are removed, and the resulting color images are a color negative.

Bottom line: You can use the C-41 developer to process black & white film. You would do better if you used a solution that is optimized to develop black & white film. You should follow the developing step by a stop-bath or water rinse. Next you fix the film using a typical black & white fix bath. The finished film should then be washed in running water to purge it of the processing chemicals.

If the black & white film is treated with the bleach-fix blix, all your images will be destroyed.