The answer is no, there’s no mention of nonbinary in any official Pokémon media. When a Pokémon is genderless, it’s simply genderless; that’s how it’s been worded in hand guides, games, etc. Those Pokémon typically don’t have a breeding group
As a nonbinary, genderless and nonbinary aren’t the same. Genderless *can* fall under nonbinary, but not always
I’d also like to add that gen 2 came out in like 1999, when gender identities weren’t as well known or established as they are today. What gamefreak meant by genderless was likely “sexless”; the inability to have reproduction i.e “desexing a dog”. Today, genderless means someone who does not belong to a particular gender identity, rather than not having sexual organs. Nonbinary and genderless people can still reproduce. Gender =\= sex (reproductive organs)
It would be idiotic to apply LGBT, human, terms to a 90’s videogame about fighting animals.
I’m not posting this as an answer right now but I might later when I can pull up the proper sources