I would think about it, but then I'd say no.
Why?
This season we got Olynyk with what - the 13th pick? He's a 7 footer with excellent passing skills, excellent hands, excellent foot work, an inside-outside offensive game (even if he's struggled so far) and he's also so far been a better rebounder than expected (about 10 per 36 minutes). He is a guy who would add some value to any potential trade, yet even if we kept him he would probably become a very solid starter for years to come.
Last season we chose Sullinger and Fab with picks up around the 20s. Sullinger was a gamble because of his back, but right now he's starting to look like one of the top 5 or players of that draft and is arguably our second best (at the very least third best) player. Another guy who would add significant value to the Celtics either in a trade or on the court.
Fab was a gamble and everybody knew it, but Danny took a chance on a 7 foot, 260 pound big man with decent mobility and excellent shot-blocking skills. Fab never worked out (at least not yet) and so that was somewhat of a wasted pick.
Before this Danny chose Bradley with a pick which was (from memory) in the teens. Bradley has turned out to be an extremely athletic guard with elite defensive skills. While he's not yet a big asset on offense, he does contribute there (13 PPG on around 44% shooting) and he's rebounding pretty well too. Another young guy who could add significant value to any trade, and who is also a good asset on the court.
That's four guys who have been selected between 10 and 25, and three of those four guys look like they will add significant value to the team either a trade asset or a roster asset. If we combined all three of those guys in a trade, we probably get a pretty good player in return.
Lets say those picks were all last season, and we traded all four of them for the #2 pick, and in return we got Robinson. Robinson was predicted by most to be one of the most surefire players in that draft, yet he's turned out a bit of a dissapointment...it would be fair to argue that Sully is the better player right now. A combination of Sully, Bradley, Fab and Olynyk would be infinately more valuable than just Robinson.
Ultimately it would depend on how high the picks are. If every one of those four picks was likely to be in the 25-30 range then I'd be much more likely to do it...but even then it's a gamble. If those picks are spread between 10 and 25 (10, 15, 20, 25) then there is a very high chance that you would get one or two very good starting players out of those four picks, and there's even a decent chance you'll pick up a future All-Star (think Boozer, Arenas) with one of those picks. In order to get more value from your top 3 pick then from those four first-rounders combined, you would pretty much have to get a bonafide All Star out of that top 3 pick. Any less and you have got the worst end of the deal.
Now, even if you don't get an All Star from one of your 4 first rounders, you will probably get at least two solid starters and one capable rotation playerout of that. You cold probably trade those three guys and get a borderline (Josh Smith, Monta Ellis, etc) or potential future All-Star (Bledsoe, etc) without much trouble. Just more options there.