No, he wouldn't. He's The Starscream.

Okay, quick rule of thumb? To qualify as being The Evil Prince, they probably have to be a prince.

Well.... he was married to the (elected) Queen, so I suppose in the crazy political system that was the Old Republic he could have been the prince consort or something like that.

But Occam's Razor says that Vader is not an example of this trope since he's not of royal blood trying to "jump the cue" (especially since the Emperor didn't have his title by lineage either).

She wasn't queen anymore when he married her. She was just a senator.