Can 300mW or 500mw engrave white paper?

Hey, I was searching for this, but could not find anything that would tell me.

I am planning of building homemade laser engraver, but I am not sure which laser to choose. 1W lasers are too expensive, so I was wondering that 300-500mW could be enough. But can I engrave white paper used in copier?Will 300 or 500mW be able to engrave to the paper?

Thank you