Batman has incredible willpower; he is shown to have done a lot of things normal human beings cannot do/do not do. Can he be considered as an X-Man? Or does he fit in the category of people who can be admitted to the X-Men Academy/School/University?
See the existing question: Has there ever been a member of the X-Men who wasn't a mutant?.
Specifically, we want to bring up Moira MacTaggart and Stevie Hunter. Both were non-mutants without any sort of super power. They were still both considered members of the team, even if they didn't fight side-by-side with the rest of the X-Men.
So, assuming the DC/Marvel Universes ever collided, there is no particular reason why Batman could not end up a member of the X-Men. I'm not really sure what his "willpower" has to do with anything though. Batman is a formidable fighter and incredibly smart; He would be a great asset to any team.
I can offer a purely out-of-universe answer - Batman belongs to DC Comics while X-Men are a Marvel property, so Batman will never be an X-Man or student.
In universe Batman could not be considered an X-Man without explicitly being part of the troupe, and willpower alone would not get someone admitted to the Academy. The non-mutants that have joined the X-Men have been superheroes in their own right. Batman may get admitted but it would be because he's Batman, not for his willpower.
As described, no.
I am not sure that "incredible will" counts as a superpower enough to enter the company of the X-men. However, given all that Batman brings to the table, even as a non-mutant, I am certain he would be welcome.
Banshee and Storm lost their powers and remained members of the X-men because of their training. Banshee had the training of an accomplished espionage agent (Interpol) and police officer. He also had excellent fighting skills. Storm's training was more on-the-job but was no less rigorous. She was a formidable thief, later mastered security systems, hand to hand combat training by the Black Panther, Wolverine and Charles Xavier. She was an accomplished marksmen and has an innate superior resistance to psychic abilities.
Would they have been inducted if they had not been mutants is debatable, but if someone had showed up at the door with the skills, training and capabilities of Batman, I am certain Charles Xavier would have wanted to know why Bruce Wayne wanted to train students at the Academy, but would certainly have given him a seat at the faculty desk.
Batman has trained, Robin/Nightwing, Red Robin, Batgirl, Red Hood and Cassandra Cain (to an extent). All of them are formidable non-metahumans who have great leadership, tactical, and strategic planning skills, as well as superior fighting skills and abilities. All would be an incredible asset to the X-men.
Seeing how Batman manages to keep a seat at the table of the Justice League, arguably the most powerful metahumans on the DC Earth, he certainly should be able to hold down a seat with the X-men.