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Usually the "black and white" is a transfer from film or photo material. It is not going to be greyscale in the computer (or YUV) sense of the word.
If you strip the chroma, you will loose that "color" tone of the source, and it is likely not-so-insignificant alteration. So I would not do this, unless you are dealing with actual digital cap of a greyscale computer image and you know that for sure.
Basically, think of "sepia" photos. You also ruin those by insisting on saving them in "BW/greyscale" format.
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