Joseph Johnston would have still had an ugly hand, cards wise, against the Union forces, but I cannot see how replacing Bragg with him would not have been an improvement for the Confederates.
Even in the laxer era of military command etiquette of the 1860s and ACW, it takes a lot for your subordinates, who are fellow generals with military and war experience, to want to turf you so bad they are willing to put their names to it in writing and appeal to someone they know will not likely take their side. Bragg was a horror-show. Usually when a general has the interpersonal skills of a grumble-lord, he is forgiven if he wins (see: Belichick, New England Patriots for the civilian variant), but if he's not winning, all the little things you force yourself to overlook with a sigh come roaring out with a vengeance.
The relationship Bragg had with his direct reports was poisoned, which meant his orders would be disobeyed where they could be disobeyed, because that's pure human nature and politics. I'm not saying his generals and staff were throwing the war, but I'm saying if you piss off your direct reports, they will irk you back any chance they can get. These are men with considerable pride and Bragg rubbed them the wrong way. It is also cannot be good for morale of any officer or soldier in the army to know there is chaos at the top. Here you are, giving it your all and fighting "the good fight" (from the Confederate view), and the a-holes above you are sniffing and acting offended at one another. Johnston was not just a good general, he was perceived to be a good general, which matters as much if not more than any actual skillsset.
Also, it is worth noting Joseph Johnston had, at the time, a great relationship with noted blowhard and apt-to-go-rogue PGT Beauregard (their troubles started after the War) when PGT was under his command and gave him remarkable leeway once he was sure of PGT's skills and/or thought PGT had a better plan and ideas. To go from a Bragg horror-show to a players' coach such as Johnston (to complete my football analogy) would have had to have reinvigorated the Army of Tennessee.
I don't know how much better (from CSA perspective) Johnston does, but once again, he would not have done worse in my view than OTL Bragg.