No they were just a little bit under the tax before the trade. This opens space for them to sign some of their two-way players - Orlando Robinson has been good and has completely taken Dedmon's role. They'd also have room to add one more player for their 15th spot without going over the tax. Of course there's also the possibility of creating breathing room for a larger deal.
In any case Dedmon was frozen out after the massage gun throw. He wasn't going to play a single minute for the Heat anyway.
Doubt he suits up for the Spurs. Dude has been unhappy everywhere he's been - Orlando, Spurs, Sacramento, Miami. He has some serious anger issues.
The best way the Spurs could use him would be by using his contract in another trade before thursday.