I think with the current lasers it might be tricky - it definitely wouldn't vaporise copper. You may be able to spray-paint it black, burn off areas that you wanted etched, and then etch the PCB.
Having said that there's no reason to use a laser - it might be possible to put an engraver on a plotter (maybe one a bit less flimsy than this) and use that to mechanically cut the copper (and perhaps also drill holes!).
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I think with the current lasers it might be tricky - it definitely wouldn't vaporise copper. You may be able to spray-paint it black, burn off areas that you wanted etched, and then etch the PCB.
Having said that there's no reason to use a laser - it might be possible to put an engraver on a plotter (maybe one a bit less flimsy than this) and use that to mechanically cut the copper (and perhaps also drill holes!).