I am sure it is possible but it is not something I have ever tried.
I suspect that the final result would be far from satisfactory as there is bound to be some scorching / charring of the edges of the topcoat and the entire surface (and quite possibly the entire thickness) of the undercoat.
Perhaps a subject for experimentation ?
Tweakie.
Spent a few hours researching this, couldn't find an answer thus far so perhaps experimentation might be the order of the day.
What's your take on Fiber lasers? I'm only starting looking into them, but they appear to be superior to CO2 lasers at least for thin materials. Although they appear to be a fair bit more powerful than CO2 lasers which doesn't bode well for simple engraving work. The main thing that interests me with fiber lasers is the fact that you don't need to spend a long period of time setting up all the mirrors (and are therefore also more reliable in exploitation) and they appear to last longer as well, so these seem to be a much cheaper alternative all around.