@dwardio is being sensible, working with unknown materials can be risky. That said, I’ll chime in on the “absolutely not”, my take is more of an “absolutely, maybe”.
Quick disclaimer: I’m just a guy with a laser and just enough knowledge to be dangerous. Take my and anyone else’s safety recommendations with that in mind — it’s up to you to decide what risks you are comfortable with.
It’s a chemical hazard
Nearly everything you laser produces gases or smoke that you should avoid. If you have good ventilation I don’t think this is particularly worrisome compared to other plastics. I’d need to check an MSDS to be sure, but that’s my gut feeling.
It’s a Literal Fire Hazard
Any material and especially any plastic is a fire hazard. Fire risk is a broad topic but to me has a lot more do with your design and your settings; pretty much any organic material can be made to ignite if you use the wrong settings and/or the wrong design.
As for it burning aggressively, I’m not sure if this particular form of styrene does or not. As most of us probably know fire requires fuel, heat,and oxygen in the right ratios. Expanded styrene, like polystyrene foam, has air built into it and burns quite aggressively, as would especially thin sheets of higher density styrene — the thin material has greater access to oxygen. For a thicker piece that you might use in a model? I’m not sure how aggressively that would burn. I’d use caution but I would think it would be manageable.
Heck I’d probably take a small piece or scrap outside with a lighter and give it a whirl to just see how it burns in a safe test.
And just to be clear, @dwardio is right: fires with plastics are serious, they produce more energy per pound than most other fires with laserable materials like wood. Caution is warranted whenever working with plastics, even ones that behave well like acrylics should be watched carefully when lasering.
It Ruins Your Bed
I’d qualify that with a it *might* ruin your bed. If you’re using the right settings you shouldn’t turn your plastic into slag. If you’re being particularly cautious you could line the tray with aluminum foil while you’re testing, if you happen to melt the plastic it would drip onto your aluminum foil and save you a messy cleanup.
Nor will you make excessive smoke and/or soot, especially if your settings are correct and your ventilation is working properly to evacuate the gases as they’re created. I would find it surprising if this was any messier than say MDF or laser rubber stamping material: both notoriously dirty, both will catch fire if you’re not careful, and both emit noxious gases when lasered that you should not breathe… and yet we don’t say you should absolutely not use them.
Do I think that the skull will laser OK? I don’t really know, @dwardio and others are right, styrene isn’t always the best target for lasering but there are many formulations and lots of different settings to try. If it were me, I would start with high speeds and low power and work my way up to see if you can get a good engrave without excessive melting or any hint of fire. Luckily it sounds like you probably have spare material to try it on in the form of ruined previous models or even the leftover bits that aren’t part of the model itself.
It may be that there’s no good combination settings that will get you the result you’re looking for. You may need enough power to get it to be sufficiently deep but that amount of power might be enough to also melt it or discolor it in a way that you’re not happy with. Multiple passes at lower power might be a good option, it’s just really hard to say without trying it.
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A lot of the sentiment about material safety that I’m expressing here is previously written up in number four on my FAQ. Here’s the link in case you want to see a more general write up of my thoughts.