With today's loss to the Miami Heat the Celtics seem pretty destined to not finish in the top 6 of the Eastern Conference and thus be forced to participate in the play-in games. There is a chance Boston could fall to #8, but even then you'd still be in the same situation of having to win one of two games in the play-in tournament.
The chances of the Celtics falling to the 9th place are extremely remote. The Wizards would have to win out the rest of the way AND the Celtics would have to manage to lose multiple games.