Yes just a single exposure to asbestos can be harmful to your health.
However for most people being exposed to a small amount of asbestos a single time or a couple times is not harmful.
Although it may affect you years down the road.
I've accidentally breathed in some asbestos when in an attic working on an old vent pipe which I though was just cement around the pipe.
It turns out that when I moved the pipe around some asbestos dust came out into the air.
I didn't move it around too much but just enough to remove it and then replace it with a new non asbestos pipe.
When I brought it down from the attic my friend told me that it was actually asbestos.
I got tested later at the doctor and they said I was just fine but I could be affected by mesothelioma years down the road.
Now I am very careful and wear respirator masks when near anything I think is asbestos.
Mesothelioma from Asbestos exposure is a serious thing that can kill you.
If you've worked in any manufacturing or construction and were exposed to asbestos you should get tested and if you've contracted mesothelioma cancer then can and should get a mesothelioma lawyer who can win you a settlement for the mesothelioma that you came down with from exposure to asbestos.