Budweiser, you lose Bird Rights to Pierce if you waive him, because he would not have completed the last year of his contract. See http://cbafaq.com #32. As LC said, we could only sign him with cap space or an exception.
It's a tricky situation. To be fair, that question is about gaining Bird Rights, not losing them. So I wonder if the Pierce situation is a bit of a loop hole. For example, Pierce would have essentially finished the prior season with the Celtics, and waived even before free-agency begins...
Further in that question:
"Once Bird rights are established, they don't go away unless the player is renounced or signs with another NBA team."
Since Pierce wouldn't be renounced, or signed by another team... he doesn't lose his Bird Rights, something he had already gained.