I think it's theoretically possible, but very very difficult. Here is how I thought it through:
We trade for Horford, something like Thornton, Olynyk and Zeller with picks. Renounce all of our FAs except Rondo and that leaves our salary at ~$63M including Rondo's cap hold. We then stretch Wallace which gives us about $10M in space under the projected 2015-16 cap. If Green declines his option that gives us a full max contract worth of cap space. At this point, we sign Gasol to the max, use Rondo's bird rights to sign him (maxed) over the cap and then offer Green the full MLE (about $5.5M). At this point we're paying tax. Before any draft picks are signed we're at $84M in salary. Our picks will probably be gone in the Horford trade so we might not add salary there, but filling out the roster with minimum guys will be costly. We'd probably need at least 1 spot up shooter. Think Dunleavy, Neal or someone taking the minimum to play here.
Our new roster looks like:
Rondo ($22M)
AB ($7.7M)
Green ($5.5M)
Horford ($12M)
Gasol ($22M)
with Smart ($3.4M), Young ($1.7M), Turner ($3.2M) and Sullinger ($2.2M) coming off the bench.
So in answer to your question, no it's not really possible. Green would have to be okay cutting his salary in half to compete while no one else does (unlikely in a SF weak market) and we'd have to convince the Hawks to trade us Horford and convince Gasol to sign here. It's just too many dependencies.
I'd settle for just bringing in Horford. His $12M salary is really cost-effective and he's a legitimate under-the-radar superstar. A starting 5 of Rondo/AB/Green/Sully/Horford is a playoff team in the East and it leaves a lot of flexibility in adding guys around them.