Strike him down and take your father's place at my side.
Vader in TESB:
Luke, you can destroy the Emperor. He has foreseen this. It is your destiny. Join me, and together we can rule the galaxy as father and son.
--
While the rule of two is not unknown to get a little bent or outright violated at times, it just wouldn't happen here, regardless of the scenario. Vader wanted Luke for himself, Palps wanted Luke for himself.
Palpatine himself was never going to die when Luke tried striking him down -- that was just the initial "can he be turned" moment. But had Luke actually killed Vader during his rage-fit, then yes, he would have undoubtedly become Palpatine's new apprentice.
...There's also the possibility that a 'dark side' Luke might've tried to kill/usurp Palpatine immediately afterward, but that wouldn't have gone in his favor. At all.
In universe, the Rule of Two has existed for thousands of years(since Darth Bane's reign)... But it was never directly mentioned on-screen until TPM.
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"I am tired of Earth. These people.
I am tired of being caught in the tangle of their lives."
But Vader killed Palpatine? Luke wouldn't have been able to? I suppose if we take Vader's feasance to Palpatine as a truth, I would also agree that Luke wouldn't be able to defeat both of them simultaneously.
But if Luke confronted Palpatine on his own? Luke wouldn't have been able to challenge him?
I was somewhat offended that the Superbowl commercial directed the audience to the internet, so I didn't bother watching the trailer until it came up on one of my feeds but this actually looks promising:
I feel like I really need to finish season 2 of Loki.
It depends what you mean by "challenge". If you really stretch what we know about canon power-levels, then Luke may have been able to put up a fight, but he certainly didn't possess the necessary tools to beat Palpatine one-on-one during the RotJ-era.
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"I am tired of Earth. These people.
I am tired of being caught in the tangle of their lives."