If Darth Vader allowed Luke Skywalker to die, what do you think would have happened to the Rebel Alliance?
Unless there were hidden Jedi throughout the galaxy, then the legacy would've died with Luke. But to answer your question, the Rebel Alliance would've continued fighting, down to the last person, because they fought for a cause, not for one person.
Assuming that was all reality, the Rebels would have continued to fight. Luke was a hero, but not the only one.