This question has been asked a few times so I thought it may be good to do a write-up about it so that this information is readily available to everyone. The short answer: Sure you "can" process PVC and vinyls in a CO2 laser. You can also cut your toenails with a circular power saw. SHOULD YOU cut vinyl in a laser?
NO. NOT. EVER!
There are a number of reasons why you shouldn't and we will cover those in this article as well as provide supporting documentation, images, and data in case you want to dig into the details.
This is (or WAS) a $30,000 Epilog Legend 36EXT that was used to cut vinyl stickers. The hydrogen chloride gas created by the lasing process turned into hydrochloric acid and, even with a more than adequate exhaust system, caused irreparable damage to the machine. These deadly corrosive fumes were also vented outside into the open air without thought or regard to the possible effects. The machine, exhaust ducting, fan, and vent area were all in similar condition. It would have been cheaper to buy a $400 vinyl cutter (or even a $2000 graphtec) than to sacrifice a $30,000 laser engraver.
Although polyvinyl chloride (PVC) can in fact be cut with laser, the thermal process produces hydrochloric acid and toxic fumes. For this reason, we advise you not to use laser for cutting PVC in order to prevent corrosion of your laser system and to ensure the safety of the machine operator. - eurolaser
Here is another laser suffering from the same fate. I do not know the specifics of this particular case but I can safely say the end user was probably surprised at how rapid the degradation was.
When PVC is heated it releases hydrogen chloride gas (which has almost identical toxicity and properties as chlorine gas), among other things. This mixes with the moisture in the air and the result is hydrochloric acid. It is toxic to humans and corrosive to most anything it comes in contact with. I am sure you could filter it out of the air and everything would be fine... except everything between the source and the filter that is. Even a very high volume exhaust would probably just lengthen the time it takes to do damage but it won't stop the damage from happening. You are much better off mechanically cutting PVC instead of lasing it.
IT IS VITALLY IMPORTANT THAT YOU CORRECTLY IDENTIFY ALL SUBSTRATES YOU PROCESS AND RESEARCH THE MSDS AND OTHER REFERENCE DATA.