I envisioned three possible values of draft picks: better player talent, cheaper pay, and increasing options for the future.
The main negatives of uncertainty in player development and the time needed to develop.
But had really no great idea on how to weigh them.
However, I came across some great articles, particularly http://fivethirtyeight.com/features/how-much-is-winning-the-nba-draft-lottery-really-worth/ and http://www.82games.com/barzilai1.htm, that helped clear the picture more. They really narrowed it down to simply how much cheaper a drafted player's results are compared to the same results from free agency.
Averaging from 538's table of net profit per pick... it appears that as of 2014, a random first round draft pick was a gain of about $13 million dollars salary over 5 seasons on average, or about $2.6 million per season. Which is about 4% of a team's cap (now ~ $3.1 million, next year probably near $4 million). Second round picks are worth probably at most $1.5 mill/yr based upon the graphs, probably less.
So... if the interest is trying to be good, it looks like $3 mill this year would bump you around 20-40 players by salary this year... or allow you to improve one player by just under 1/4 of the league's talent.
To upgrade from about the cheapest end starting salary (#150 = 4.3 mill) to a max contract (this year 1st year = $18.5-26 mill based on experience, higher for certain players) you'd need the benefit of about 5-7 average draft picks.
So then looking into the Celtics... based on http://espn.go.com/blog/boston/celtics/post/_/id/4716912/bostons-pile-of-draft-picks, you'll gain 5 more extra first round draft picks by the 2017 Draft... so in theory seems decent.
In a totally random world, you'd expect picks of about 3, 7, 10, 13, 17, 20, 23, 27. So if the team had designed their contracts to absolutely start over from scratch about now... you'd get those 8 picks locked up for a 2nd year cost of only $14 mill total! Then you could afford to add on maybe like a... Kevin Durant max (should be ~23 mill second year^)... plus a DeMar DeRozan max (~22 mill second year^)... and still have 11 mill left (perhaps sneak in a free agent of the likes of Aaron Afflalo [8 mill], Danny Green [10 mill], or Rondo [9.5 mill], or get a team like Washington to trade someone like Gortat [11 mill] for later picks\contracts if they want to rebuild).
^ - These numbers will all change a bunch this year due to the salary increases. But the thing is, assuming the distribution by talent stays the same (it generally should given min\max\rookie and such are all tied to salary cap), then the approximate player classes you can get and what a draft pick is worth shouldn't change. So you'll see bigger numbers than those I gave for the players, but have a higher salary cap to match.
So that's an average expectation of how things could be worked. You'd also quickly be going well into the luxury after a couple years, and so your owner would probably have to be willing to pay a lot extra. The economics from an ownership standpoint is a whole nother ball game. Getting these picks meant rebuilding, and that can be some really poor years. But then, being a middling team won't make money like being a star team. So a whole lot of other calculations to it from the ownership standpoint. Basically, is it financially worth it to be good? Considering league minimum is 90% of the salary cap, you'd think generally yes, unless you have a really consistent fan base.
Anyways, if it did all build together as I've suggested, the team would then be mostly limited after that to building through the draft, min deals, and mid-level exceptions. Not a ton of flexibility once that team starts growing (and that's why most teams don't consistently contend anymore?)
But feasibly, it could be done. Though your additional extra pick last year ended up being low, looks like this year you'll get a good lottery pick from the Nets, plus a fair pick from Dallas, and your own. I guess your Minnesota pick is turning into two more second round picks (gosh!). But then you've still got what are probably fair picks from Memphis and the Nets to come in upcoming years (plus your picks and that pile of second rounders).
But then, in all this, I didn't even look into what the Celts have already built. #4 in the east, mighty impressive. With $20 million cap room next year (based on current cap). Actually, $32 mill if you elect to part with Amir. Thomas, Bradley, and Crowder locked up for two more seasons.
So you could maybe resign one or two of Turner, Zeller, Sullinger... and still get a max player contract... and sign most of your rookies (doubt you'd want 8, if you still have that many picks this season!).
And again, the numbers of course go way up for the cap this year and next (and thus the max and rookie contracts), but it's still the same general situation because it all balances, salary increases vs cap increases.
Players honestly probably won't want to sign long deals because of the big 2017 increases, but in a sense that only helps you. If you can woo a star for a year based on what you have... then you can have the inside track to sign them next year... or be free to part ways and pursue other max contract guys while enjoying the same great cap situation. Usually players are FORCING long-term deals as it benefits them with security. So that you don't have to do that is just generally a plus. Especially if you're good next year (so people want to come your way).
Plus the picks allow you maneuverability to trade for players or perhaps for picks further on down the road.
Yeah, picks certainly aren't the end all. I don't think the most explosive resurgence stories (Heat 2010, Celtics 2007) were heavy on picks. But then there are situations like the Cavs last season or the Magic in 2000 (McGrady+Hill... perhaps close on Duncan) that still show potential is there.
A lot of luck involved when it comes to draft picks. Having them be high. Having the players picked work out. Getting stars to invest in you over clubs. Picking up the right cheap free agents. But overall, it seems economically workable. Though it depends what you give up to get them, of course.
But so far... you're looking mighty good!
Addition to better answer one of your questions:
The problem with rebuilding without giving up talent is usually your options are very limited. If your decent, you're not getting great draft picks. And you don't have much cap room to sign players, all the while dealing with restrictions based upon your current roster (and player desires). That the Spurs turned the 28th and 57th picks into two of their cornerstones was a shot in the dark. And now Leonard at at 15th. Not everyone can do that, it just isn't possible: there aren't enough good players available to be found that low! So finding the stud GM\staff\talent scouts cannot be undervalued.
And the bonus that elite teams also get players (their stars and FAs) to sign for less helps extend their reign, as San Antonio has done a fair bit of too, I believe.
Most teams will "rebuild" just by sliding towards mediocrity as their stars age and retire\move on. Does selling the entire farm for picks give more potential for a return to elite success? Don't know if we can tell given there are so few real fullblown cases. The numbers given show there is some potential. But the real answer probably is: go where the value is. If there's a lot of teams moving towards rebuilding, then the buyers market will land you talent for cheaper. But if there's a lot of teams seeking talent, you might have an opportunity to stockpile picks. It's not so much what you do as what the other teams do, and then what you make of that situation.
But I certainly can't think of many San Antonio's at all in this day-and-age in the NBA. Much like the Patriots. You absolutely have to mine low picks in the draft and free agency insanely better than the league. And so then it just can't be a common thing!