So I almost had a successful cut today. However I will say I think it is possible but I think what it will take is multiple passes with cool down periods between passes. If too many passes are made too quickly it melts back together. J-tech posted a blog post a while ago about cutting abs with a 2.8 watt laser and they did something around 25 passes at 150 mm per minute. I assume I will need to do something about the same but with cool down periods.
I did burn a whole through a piece, albeit accidentally. So I know it is possible.