The NBA draft lottery began in 1985. In the 28 years of its existence the team with the worst record has gotten the #1 selection only 4 times (14%).
Since this is a deep draft, maybe the C's would be fine with the second, third or fourth pick? Of the 84 players chosen in spots 2-4 since 1985, only two of them have ever won a title with the team that drafted them, and both (Sean Elliott and Jason Kidd) did it many years later after having been traded and then brought back. No player selected 2nd, 3rd, or 4th has ever led the team that drafted him to a championship in the lottery era.
The Grizzlies had top four picks 5 years in a row from 1996-2000 (#3, #4, #2, #2, and #2 again), and they followed that up with consecutive 23-59 seasons in '01 and '02.
And even if the Celtics do get the #1 pick, other than the San Antonio Spurs, no team that has ever won the lottery has gone on to win a title at any point afterwards.
In fact, only 4 top lottery selections (again 14%) have ever helped carry a team to a title (two Spurs, David Robinson and Tim Duncan) and half of them (Shaquille O'Neal and LeBron James) didn't do it for their original franchises. If Boston did get a game changing player at #1, whose to say he'd stick around long enough to win a championship?
Based on these stats, tanking might bring the C's a 14% chance of getting the #1 pick, and another 14% chance of him taking them to a title some day. That puts the odds of success at roughly 2%. I realize this math is far from perfect, but it's crazy to ignore the past when planning for the future.