Everyone wanting Sale or Archer or Gray seems to forget that the Braves will have to compete with others who will want those assets as well. And many of those other teams will be in much better positions to compete for pennants than the Braves truly are right now. Teams like Boston, LAD, Toronto, Baltimore, NYY, Cle, Det, Sea, Tex, Hou, Was, NYM, Cubs, Cards, Colo all are in a better position to compete in 2017 than the Braves and will be looking to improve their odds. Not all those teams will be primarily looking for pitching and not all could out-bid the Braves but I could easily see teams like Boston, LAD, SEA, HOU and COL being all over high end pitching should it become available. Even teams like Baltimore that the Braves could clearly "out-prospect" may be willing to move significant ML talent to bring back a high end pitcher as an example.
So, while the Braves might be able to acquire a Sale or Archer or Gray, chances are they would have to over pay as opposed to finding a bargain.