The poison pill has nothing to do with it. Even if Pritchard hadn't signed the extension the same thing would be true. Due to being a supertax team Boston only has a 10% buffer in trade, and Pritchard plus any two guys from the end of the bench are about 500-600k short of the necessary total. You can get there by including Walsh.PP+SVI for Caruso doesn't work. The Celtics would need to add 2 more players to get to the number, because PP is poison pilled (he counts lower as dollar value in the trade for the Celtics than he does for the Bulls.)
EDIT: As a note this gets easier in the future as the MLE can be used in the same manner as a TPE (starting next year, I believe).