What if Luke hadnt channeled the dark side?

What if, "If you will not join the dark side, then perhaps she will!!", didnt inspire dark side rage in Luke and he lost and Vader killed him (which I believe he would have in that scenario)?

What would Vader have done then? No doubt he would have sought to seek out Leia and somehow try to turn her.

I think realizing how strong willed (he already knew pretty much from the mind-probe in Ep:4) she was he would have had her arrested and executed.

Or not?

Opinions?