Plus think of it this way.
Danny made the decision to tank mid season when he traded Rondo and Green (then, the teams two best players) away. Pretty much everybody expected this team to finish bottom 6 after those trades happened.
The guys on the roster knew that - they knew their leaders and best players were gone. They knew they suddenly had less talent and star power than ever. Somehow though, they overcame that by working together as a team. They refused to give up and die. By leaning each other and working as finely tuned cogs in a well coordinated machine, they were able to achieve what probably shouldn't have been possible based on their talent level alone.
Through this they all learn a lesson - that many hands make easy work. That working together unselfishly as a team, you can achieve so much more then you can as an individual. Those are the type of lessons that will make every single guy on this team a better player and a better teammate, and that will stick for the rest of their careers. You can't put a value on that type of experience.
In addition to this, they all know that it was Coach Steven's excellent work and persistence that helped them achieve what they did, so now everybody on this team has the greatest respect for a coach who (up until last season) had never spent a single day in the NBA. Again, this type of respect for your coach is something you can't buy.
That respect also filters up to management - Danny pulled the strings to assemble this team which (only one season prior) experienced the first year of a rebuild. He turned this team from playoff team, to an almost complete rebuild, back to a competitive playoff team, all in the space of three seasons. He did all that without acquiring a single star / superstar caliber player. That is beyond impressive, it's unheard of. And it's not like he did it by sacrificing the future - he build this team into a playoff team using almost entirely young prospects, and picked up a plethora of picks and a ton of extra cap space in the process. If he doesn't get GM of the year it will be insulting. Again, this all gives your group of guys trust and respect for management staff and the organisation as a whole.
So now, just by making the playoffs (regardless of whether you go deep or get swept in the first round) you have managed to build an incredible level of comradery among your players, complete respect for your coaching staff and an immense trust in your management/organisation.
Now when this team is recruiting players, all of their existing players will be incredibly eager to tell (anybody who is willing to listen) how rewarding and enjoyable it is to be a Celtic, and they will really believe it.
These things mean a lot.
If you're a young, highly sought after free agent, looking to sign a long-term contract, what do you look for?
1) You want a coach who will respect you
2) You want a good group of teammates who are selfless and hard working
3) You want a management and ownership team that know how to build a winner
4) You want to a team that has shown it can be competitive, and is only getting better (hence indicating the potential to be competitive for years to come)
Last year Boston didn't really feel like they had any of those things, and if they were a lottery team this year that impression would have remained. Now they make the playoffs, and suddenly this team looks like it has all of the above.