Does he seriously think this will help him?
Yes. The point is to say something that eats up each news cycle.
Trump says: Ted Cruz can't be POTUS because he's Canadian. The media spends a week talking about it.
Trump says: Ted Cruz cheated in Iowa. The media will spend until Saturday talking about it.
At the NH debate, Trump will accuse Cruz of something else. The media will spend its time on that accusation.
If there is a lull in the coverage, Trump will say something about Megyn Kelly or some other "journalist" so the media can focus on that instead.
The common theme is the media talks about Trump for free while repeating the nasty accusation regardless of the merits.