Warning (Added 2015) Some of the documents that we previously received through FOIA suggested that all major manufacturers of color laser printers entered a secret agreement with governments to ensure that the output of those printers is forensically traceable. Although we still don't know if this.....
Yes, assuming your printer has a black cartridge. (Otherwise, it's because it legitimately needs all the colors to reconstruct a shitty black -- I don't know if they still make printers like that, though.)
"Rich black" in CMYK is one thing, but not what I was talking about. Am I misremembering that some really old inkjets used to be just "CMY" (or maybe a slightly different set of three pigments, but either way no K) where they had to mix all three to get an approximation of black, and do any like that still get made?
(It's been long time since I've paid attention to any kind of printers other than lasers, LOL.)