An interesting question; I cannot say for sure that this is possible, but it sounds quite reasonable to me.

Just the same, a very similar phenomenon called a broncholith, which is more rare, can be a sign of a fungal lung infection, such as histoplasmosis. I really just found out what tonsilloliths are; I had always wondered what I was coughing up since I was about 17 years old (ten years ago). When I found out about tonsilloliths, I was shocked to learn that they form in the crypts of the tonsils, and you cannot get them if you have no tonsils, which I do not.

If you are coughing up tonsilloliths or feel that one may be stuck in your lung, you should consider having a chest x-ray to be sure that you don't have histoplasmosis or aspergillus fungi in the lung.

If you spend any time in caves, chicken houses, or playing with birds or bats, or digging in any soil that may be contaminated with feces from these animals, you have likely been exposed to such fungi. Perhaps a blood test would be a good idea.

Of course, it has been over a month since you posted your question, and you may have already received some diagnosis from a health care provider, which I am not.