Late answer to this thread, but I just came across Star Wars Trilogy: The Original Soundtrack Anthology box set which was released in 1993; meaning it is pre-“Special Edition” so some of the track titles and names allude to a universe that was not fully “expanded” in the post 1997 world.
Specific to this question, on disc 3—which contains tracks from Return of the Jedi—track 5 on that disc is actually named “Return of the Jedi” which is basically the musical cues specific to the scene in the film where Luke is about to “walk the plank” into the Sarlacc pit and then pulls a fast one—with the aid of R2-D2—and does some force-related moves including fending off Jabba’s flunkies with his lightsaber.
Which is all to say that at least at the time the film titled Return of the Jedi was released in 1983, the “Jedi” that had “returned” was embodied by Luke.
In The Empire Strikes Back (1980) he was “Not a Jedi yet…” and loses his hand—and almost loses his life—because of it. And at the beginning of the film Return of the Jedi, Luke has a new lightsaber and knows how to use it. In fact that rescue from Jabba the Hutt was the very first time anyone actually saw a Jedi do anything heroic in the classic, swashbuckling “I’m saving someone’s life…” sense and not in the sense of having endless duels with Darths and other members of the Sith.
So if you ask me, Luke’s training to become a Jedi was solid at the beginning of Return of the Jedi, but the ending was his true test… It’s not like—if in some parallel universe this happened—that Luke might have been turned to the dark side and was never a Jedi to begin with. Nope. He was a Jedi at the beginning of the film, but his confrontation with Vader and the Emperor at the end only reinforced it.