While it seems like it’s ultimately not correct, there really is no precedent to deciding this, unlike the sham immigration marriages, so I think it’s a fair question.
NYS has redefined marriage to be anything goes and nothing to do with things that usually come with a marriage. So why can’t 2 yeshiva guys, who can be extremely close to each another (without being physically close, of course) consider themselves “married”? NYS has has just destroyed the both the sanctity and definition of marriage in NYS, so the answer should depend solely on how the state legally defines “marriage”.
This is assuming there are no other halachic issues like maris ayin. I would assume there is no such issue here because “lo nechshidu yisrael lo al mishkav zachar…” so it should be obvious to any observer that this is a marriage in the now-legal sense but not one that violates any issurim which should mean no maris ayin issue.