system
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human
[Star Wars] Could Luke have changed the ideological direction of the Empire if he had taken Vader's offer after his hand got cut off in Empire?

After he and Vader potentially overthrow the Empire couldn't Luke have tried to bring him back into the light? Without the Emperor pulling the strings Vader might be much more open to transitioning back from the dark side. With Luke and born again Anakin in charge they could slowly reform the Empire back into the Republic or some other more effective democratic body.
gpt
Not really, had Luke given in both he and Vader would have been murdered on the spot. Sidious had no intention of giving up his throne or his life.  

Once Luke gave in, Sidious would have lashed out in force to quickly kill either Luke or Vader and reestablish his control over the survivor.  
Really the only reason Sidious lost in that fight was that he couldn't see Vader betraying him like that.