Boston has 9 players under contract next year, two more with team options, and 2 or 3 of its own free agents I assume it would want back (depending on price of course) in Sullinger, Turner, and Zeller. Let's say Boston brings back 2 of the free agents and plans on using Johnson and Jerekbo to acquire 1 player in a salary dump type situation. That puts the roster at 12 before the draft picks and any other free agent signings (for this purpose the 2 free agents brought back will be signed after using cap space). If Boston signs no other free agents then the 3 1st rounders will fill out the roster and none of the 2nd rounders will make the team. But I think it is unlikely that Boston does nothing in free agency, which means there is no way Boston can have all of its draft picks on the roster. Now sure there may be a player or two drafted that stay in Europe, but eventually said players will need to come over.
The reality is Boston is going to almost certainly trade some of the picks. I assume Boston will first look to trade picks for established players, but that would also require established players because a team like Chicago isn't going to trade Butler for only draft picks, it will want someone like Bradley and/or Crowder back, plus draft picks (including 3 for the sake of this discussion). Is that a better trade then moving up for Ingram or Simmons? That is the question and in that there is no easy answer, but assuming that no trade for an established star is made, I think Boston absolutely will look at moving up to 2 using 3, Dallas, and whatever else it takes. The real problem with this is, is I can't see a team that could be in 2 that is set at wing and weaker down low, thus none of them would trade Ingram for Bender (plus other stuff).