When "Promote Gray to CMYK Black is selected, all neutral and near-neutral grays in an RGB files are converted into a predominantly black color.
When this function is disabled, the grays are converted into CMYK as encoded in the target ICC profile.
The expected behavior is that only grayscale images are moved to the black channel of a CMYK image.
The only explanation in Acrobat's online User Guide is as follows:
"Promote Gray To CMYK Black - Converts device gray to CMYK."
This function should not change the way an RGB image is converted into CMYK. This conversion should be governed by the choice of source/target profiles, rendering intents, and black point compensation.