While it seems possible that flooding the market with all 100 paintings at once might crash the price down more than the tax writeoff is worth, it seems unlikely that this would happen on the first sale. The counterargument would have to be that there doesn't actually exist any outsider who would pay anything close to the claimed value for the work.
Another odd aspect of this is that once individuals own a substantial numbers of works by an artist, it's in their interest to keep the price high for that artist's works. So if a new painting comes up for auction, they would benefit by never allowing it to be sold for a low price --- even if that means "overpaying" for the new painting. So maybe the end game is that the minority owners start to sell, knowing that the majority owners have to buy, and only after all the works have single ownership (with a record of high sales prices) sales does the donation scheme happen.
Interesting. I presume others have analyzed these strategies in depth?