Offset printing of black-and-white photographs in a page with abundant color

Hi, When placing a black-and-white photograph in a page that will also have plenty of other photographs, illustrations and layout elements in color, part of a magazine that will be printed in offset, is there a rationale for preferring that gray values of that photograph are printed using only black ink or with a mix of all CMYK inks instead? The particular CMYK combination I mean is the one I would automatically get in the likes of Photoshop by converting the grayscale image to the target CMYK color space using ICC profiles. — Jorge