IMO, what makes it most likely for the Clippers to be open to a trade is if they get knocked out by Portland. If that happens, maybe they try to shake things up and move Griffin and/or Jordan. Based on the newly configured roster, maybe they see Pierce as not being quite as essential based on their new needs, especially since he'll be a year older. Then when you factor in Pierce's relationship with Doc, and the fact that Boston isn't in the same conference as the Clippers, I do think there's a realistic chance the Clippers would be open to moving him for the right price.
The question then becomes what the Celtics need to offer to make it happen, and how much Ainge is willing to give up. I think Ainge has proven in the past that, if he feels like the C's are legitimate title contenders, he's willing to use his assets to make the roster incrementally better. In the hypothetical situation of the original post in this thread, I do think Ainge might consider sending an early second round pick and/or a younger player that is somewhat of a duplicate on the 2016-17 Boston roster (maybe Olynyk, Mickey, Sullinger, Rozier, etc.) to the Clippers as the main piece in the deal for Pierce. If Pierce really isn't in the Clippers' plans, it'd make a lot of sense for both sides.