Printing normally processed C-41 film onto B&W paper can produce odd results because most B&W papers aren't sensitive to red light, and of course some of the color negative's image will be defined by red wavelengths. You might still get acceptable results, or it might end up looking weird. Just for the heck of it, I tried printing a photo I took of two people using color film on B&W paper. One person looked OK, but the other had an unnaturally dark complexion in the print, in a way that was very unflattering.
Kodak used to make a B&W paper for printing from color negatives, but it's no longer available. My understanding is that both Ilford and Oriental still have such products, but I don't recall their names. These papers would all have to be exposed and processed in complete darkness, much like color paper.
Another approach would be to process the color film using B&W chemicals. That will result in a conventional B&W negative, except that it'll have a dense orange mask. That mask will require longer exposures and perhaps contrast adjustments, but at least you won't be dealing with red information being "lost."