Sure they could have. It isn't all brute strength, as Lee had just shown at Chancellorsville. Had he shown enough cool in the field, he could have gone for Longstreet's battle of maneuver and driven Meade nuts for weeks before bringing him to battle on ground favorable to Lee, rather than jumping at Meade's good positions on Cemetery Ridge.
Lee needed a C-in-C of the Confederate Army to manage "the vision thing". Edward Bonekemper, whom I just mentioned, shows that Lee was theater-oriented to a fault, which is understandable given the fact that he was a Virginian, but not forgivable in the grand-strategic sense. Longstreet's success at Chickamauga shows what "could" have been, had he been in charge of strategic-level operations directing a campaign of defense on interior lines.
That Longstreet showed deficiencies in independent command and even as a corps commander (being consistently slow to "get up") does not detract from his grasp of possibilities. Too, he had experience as a supply officer (his last prewar billet out West), and could have done a lot at HQ to curb the excessive hoarding tendencies of the Confederate commissary system.
Lee needed Longstreet as CSA chief of staff to curb Lee's own excessive bias toward aggression, to provide a broad vision, and to untangle the GHQ mess. So saying is not to say he would ever have overcome the favoritism, backbiting, and prima-donna politics engaged in ad nauseam and to the considerable detriment of the cause by e.g. Braxton Bragg.
Meanwhile, if Lee had taken Longstreet's advice on the evening of the First Day, he'd have had a much more successful campaign in Pennsylvania. After all, it was Longstreet who'd told him where Meade was -- thanks to Pete's man Harrison.
Ok, ok, we are not communicating. I'm saying BARRING an acceptance of Longies' arguments for a war of maneuver. But then that wouldn't have been "winning at G-burg." It may have been winning elsewhere, but not there.