Cockroaches and Air Cons

Can roaches get into the room via the air conditioner?

Once or twice before, after switching on, a sudden (huge!) dark shadowy movement signaled invader. Usually the black flying kind and seemed to emerge and fly from the air con.

Is that possible (I mean, like climbing up inside pipes to the indoor blower), or is it more likely the roach was 'hovering' and got blown across the room after switch on?

Most likely the cockroaches are already living in your home (rather than coming in from the outside) and that the cockroach was hiding in the aircon when you turned it on it got blown out into the room. Get yourself some poison bait and roach motels and that should help prevent future invaders.

But theoretically, yes, a cockroach could have gotten in from outside via the air conditioner, and there are a few steps you can take if you are worried they might be coming in that way. While the indoor and outdoor parts of the aircon are connected by a closed system of pipes containing coolant (air doesn't actually move between the two fans), there are two places that can serve as an entrypoint from the outside. The first is the condensation drain hose (the hose that drips water outside while the aircon is on), and second is the actual hole in the wall that all the pipes travel through. The hole in the wall should have sealing putty placed in all the gaps and sometimes its further covered by a plastic cover. Check the outside wall and if the putty is cracked and falling out, or simply missing, then you can get some more from your local home center to replace the seal. For the drain hose they sell an endpiece with a built in grill that should prevent large insects from getting in. I don't think the hose is a big concern though, and whatever you do don't plug it up or you'll have water flowing into your room.