You had Francouer as THE guy before them. There is always a player or two who are supposed to be the franchise saviors. But, you have to look at the supporting cast and what is available in the high and low minors. If you look at what the Braves have done in the draft the last 4-5 years, they have taken low risk low ceiling guys early, have stayed slot on bonuses which has precluded many later round steals and have mostly exited the international market. The best thing the farm system has been able to produce over the last few years has been relievers. The bats have all been fringy at best or outright miracle picks (Gattis). The starters have been just OK with Wood being the best.
Teams that get old and bad at the ML level and bad at the minor league level go into long stretches of being terrible. But most of those teams also have major ownership problems.
Teams rebuild all the time (Oakland for instance) and bounce back strong. With the financial capability that the Braves have, solid middle of the pack, there is no reason they can't do it.