Unless there's further roster shakeup, I think the Celtics will pick anywhere from 6 to 12. They have an outside shot of the playoffs, given the conference, and if they can get there, good for them. I don't think that with the current roster they can be at the very bottom. They don't have top end talent, but they have guys willing to give their all and keep fighting, a lot of pride, top to bottom, which can't be said for a lot of teams with similar records.
While getting one of the prized top 5 picks might be a bonus, ultimately what's good for the roster is getting a center and someone who can shoot at a high level. An Embiid or a Cauley-Stein, depending on where they pick for the center position. For the shooter, it depends on who's available. Getting one of the top picks would be a luxury for this roster, and landing Wiggins especially probably wouldn't lead to an immediate dramatic impact. Randle would face stiff competition with Sully and what is hopefully a much improved Olynyk by then. So a top 3 pick would necessitate some further roster shuffling. Outside of that there are combo guards in Smart and Exum, plus Embiid.
I think that's the real sweet spot for the Celtics, but even after that there are going to be some quality players to help the team out.