I don't think this affects the fate of the Celtics' ownership of their draft pick in 2016 because regardless of the owner they will have limited ways of improving this season and next. After that it's unclear because they, like a million other teams will have oodles of cap space to play with. It seems unlikely anybody will choose their millions over a better team but who knows? Since they don't have their own draft pick for awhile there really is no reason for them to outright tank. They might as well just sign anybody who will play for them, even if it means overpaying for good but not great guys. That might make the team mediocre enough to still end up in the teens for picks.
If the NBA reseeds the playoffs so that the Eastern Conference is forced to compete with the West for spots then all bets are off.