“Air purifiers” commonly refer to some sort of particulate filter.
“But my filter has carbon in it too! It should be good, right?” you think.
No. Common residential/commercially-available air purifiers do not have enough activated carbon media, dwell time, or clean air exchange rate to handle VOCs like styrene from your printer.
Most air filters with carbon have maybe enough to filter the smells from a fart; that’s what they’re designed for.
Here’s what the CDC says about styrene (the VOC that’s most concerning from ABS and ASA):
The most common health problems in workers exposed to styrene involve the nervous system. These health effects include changes in color vision, tiredness, feeling drunk, slowed reaction time, concentration problems, and balance problems.
The safest thing to do is to vent styrene (or other VOCs from other materials) outside.
You should, of course, do your own research and make a fact-based decision based on your risk tolerance.