That doesn't really make a lot of sense in terms of keeping that team together.
As it stands now, the Spurs have a payroll of roughly $53M assuming Duncan accepts his $10M option. They still have to resign Diaw and Mills if possible. Maybe they let Mills go and run with Joseph, but Diaw must be retained. He's going to cost at least $6M a year. That gets them to $59M and leaves them with $4M in cap room or the $5.5M MLE.
Even if Duncan takes 2-years, $14M instead of 1-year $10M, that's only going to free up another $3M in cap room, getting them to about $7M. What can they really accomplish with $7M that they wouldn't have been able to accomplish with the MLE?
Spurs would be right at the salary cap re-signing both Diaw and Mills with the MLE to spend. They also will be well below the tax line.