And it may be that I should be using the PDF/X-1a:2001 preset in this case, but the same question remains: Is Color Conversion needed for a black-and-white PDF?
There isn't a way to convert a grayscale image from one grayscale space to another when you export from ID. You can do it in AcrobatPro after exporting.
If you choose No Conversion, Convert to Destination (Preserve Numbers), or Convert to Destination with the destination set as document CMYK; grayscale objects will export unchanged. If you choose Convert to Destination with a CMYK Destination profile that is different than the document CMYK profile your grayscale images will get converted to 4-color CMYK values.
With CS6 or later there is the option to export to a grayscale destination profile, but that still always leaves placed grayscale values unchanged.