No.
HP color printers use a variety of the color cartridges to create the colors that are seen on the output. Black text and images actually have a small portion of that black generated from the color cartridges too when color printing is enabled. Greyscale will allow you to print only from the black cartridge but your color cartridges will still be consumed via evaporation and general mainenance.
In other words, you can get your printer to print primarily from the black cartridge, but not the other way around.
Ink Usage in Inkjet Printers:
http://h10060.www1.hp.com/pageyield/en-019/articles/howInkIsUsed.html?cCode=us