Since analysis shows that Bragg, Johnston and Lee are not much different in terms of ability, no and yes. See Hattaway and Jones, and so frustrated was I with a lesser light that I got scans of the entire appendix and put it online:
http://historum.com/american-history/81934-most-decisive-battle-civil-war-23.html
Rosecrans does a pretty **** good job at Chickamauga, and one of his subordinates screwing up and opening a hole just as Longstreet attacked there is essentially a chance event. Would have happened to Grant as well.
Stones River? I don't see a reason why that would be different either.