Is it possible?

I,d be more worried about a meteorite hitting earth. Anything is possible. If you are really concerned and have had a broken windscreen, I,d get a decent vacumm cleaner and once again suck the air from around the vents (this would have been done by the mob replacing the screen anyway). Do it while fan is on full blast..

For the majority of broken laminated windscreens it is only the outer layer that cracks so there is really no chance of glass fragments getting into the ventilation system. Even if the inner layer cracked there would be little glass breaking away from the windscreen.

With older tempered windscreens that completely fragment - well we all know what a mess that makes - so I guess it is possible but really unlikely and have never heard of the problems you allude to. Sure cuts and scratches but nothing on breathing in glass fragments from the ventilation system.

Chris
For any glass from a hit on the outer layer of the screen will fall down and into where the water off the screen accumulates and drains onto the ground. Not sure about ducks, but the ducts, which carry air into the cab means the air has to get above a ledge, then travels through the intake duct and is then centrifugally spun by the aircon fan and would deposit at bottom near the fan. If any travelled further, it would have to find it's way through the aircon evaporator core which is thick and fine finned. If all that didn't filter any fine glass out of the airstream then not sure what would. The air is then delivered to the cabin through the dash ducting which in modern vehicles has a particulate pollen filter before the blower fan. Has to be very microscopic to get through that.
You can think about it if you wish, but I would think more about more important issues. If you get a windscreen hit, simply stop breathing in for a while until the airflow is cleared if concerned.
Associated comment.
People taking powdered drugs, unkowingly, often snort powder with powdered glass in it, The fine glass edges, specially incorporated by your caring drug supplier, cuts the mucous mebranes of nose and throat and make less drug in the mix seem more effective. A bit like Toyota, "Oh what a feeling". More hit for less drug, ripped off eh, dealer doesn't care. They don't seem to suddenly die of glass ingestion though. Pity.

I’m in the glass game (25 years now) and the risk of Silicosis is slim to none with the glass fragments you are speaking of, whether it does happen to be a late toughened glass windscreen (doubtful) or more likely laminated glass that has ‘spalled’ shards etc inside.

I would do this.

Use a good strong vacuum, preferably industrial with great suction.
Make up an end for it from plastic milk carton etc to bring the end down to a smaller fine flat oriface that can be put into the ducting.
Vacuum hell out of it.

Then cover front interior (seats etc) with disposable plastic sheet.
With ignition on, turn on demist then from outside the car reach in and turn on ignition to blast any residual out.
Anything left won’t be a problem.

Vacuum carefully dash, seats etc as best possible and you should be good to go.

.
And whatever you do Chris....... don't ever visit Maralinga!!! lol

May be more chance from a side window. Last yr on a slight corner at 100kph out of town a semi threw a rock up hitting my drivers window shattering it some small pieces landed on my shorts but it was mostly held together with the tinting. The main concern was the angle it came at which was between the ute mirror and door pillar straight at my head I was lucky, the noise was very loud wasn't that concerned about the small pieces of glass.

Blanked DPF's allowing highly toxic diesel particulates into the air are far more likely to kill you. You need to prioritize your small particle phobias better.

In the days before laminated windscreens it was common for fragments of the so called 'safety glass' to find their way in to the demister ducts either when the screen shattered or when the broken screen was being removed. There were cases of eye injuries caused when the blower fan was turned on and glass particles ejecting from the demister ducts ricocheted off the windscreen and lodged in the eyes of those in the front seats. In response to this and to avoid further claims for damages from an eye injury, the insurance Companies at the time instructed repairers to vacuum the ducting to ensure all such glass particles were removed. They also allowed the cost of doing this when reimbursing the repairer. Insofar as ingesting glass particles go, I would be more worried about an eye injury than any damages caused by ingestion and as others have said, with laminated screens today the chances of glass particles inside the vehicle from a cracked screen is negligible. Different story with windscreens smashed in an accident though where sharp glass shards can penetrate any part of the human body that gets in the way. All the more reason to keep windscreens in good condition and replace as soon as possible if any cracking occurs. As far as ingesting glass fragments goes, with all the glass food utensils/jars in use, I would guess over our lifetime we probably do swallow some glass particles without even knowing we have done so and with no subsequent apparent ill effects.