Convert CMYK (CMY are 0) to grayscale

Hello,

Is it possible to convert in Acrobat a CMYK document that is basically a grayscale document (CMY channels are 0, only K has a value) to a true grayscale document, where K_grayscale = K_cmyk (in other words, the grayscale K values are the same as those in the K channel of the CMYK document)?

Thanks.