I think cap room is very important along with having a proven star on the team already and some young talent on cheap contracts. The positive in signing free agents over draft picks is that you know what you are getting, there are no secrets or potential waiting to be untapped. High draft picks have the potential to under achieve and building exclusively around a pick is very risky IMO.
My ideal rebuild would involve keeping Rondo, Sully, Olynyk and maybe Bradley then trading everyone else for whatever you can get to help lose games (except Wallace, he isn't going anywhere).
Sure maybe these players (Rondo) may hinder the chances for a top 3 pick, but ground can be made up by signing players like Monroe, Deng, Stephenson, Hayward etc along with a top 10 pick and a $10mil trade exception. Then you wait to trade a bunch of future picks for a star player.