Most likely it will tell you to insert the color cartridge when you go to print something, even if it's just black and white. I've tried it on my Epson printer. Its worth a shot to take it out and give it a try.
I kept researching after posting the question and found out that there are 3 technologies used in HP printers:
1. Integrated Print Head (IPH) where the print head is part of the ink cartridge.
2. Individual Ink Cartridges (IIC) where the print head is replaceable.
3. Individual Ink Cartridges (IIC) where the print head is fixed and supposed to last for the whole life of the printer.
Mostly the 1st category is the one with which you can remove a cartridge and the printer will keep printing, and you can do that safely. But I couldn't find out yet about this particular model (HP Deskjet Ink Advantage 4645).
I appreciate if someone can help me with this. It has 2 cartridges:
If this is for a company, push the settings out over the network to users' machines that have the printer mapped, and lock the settings down over Group Policy so standard users cannot change settings back.