No, he's not a crossdresser (wild theory time)

Based on a few things like Lemons remark ("we're both girls") and that fact that Kazuhiko looks so good when disguised as a girl, many people have proposed that Nukkun is actually a crossdressing girl.

You could counter this by remembering that he took a bath with Sakurai at Hokobaru's house. But then you could counter-counter this by positing that Sakurai is also a crossdressing girl (he looks even more feminine) and the two were covering for one another. Which makes the scene where Tieara wanted to bathe with them even more hilarious than it was.

However, there is no getting past scene where Tamaki scared Nukumizu in the boys room as he was taking a leak, I'm afraid there's no getting around the fact that Nukumizu is a boy, although a strange one.

Ah, but we're not done yet. The shiny new theory is that Nukumizu was originally a girl (tomboy) who badly wanted to be a boy. And finally, in middle school he/she prevailed upon rich parents, and had gender reassignment surgery. This usually consists of surgically reshaping girl parts into boy parts. Making her dream a reality.

But this had unexpected repercussions for Kazuhiko in middle school. All the boys and girls who had known her as a girl, shunned him completely as a boy. With rare exceptions like Lemon and Ayano, Kazuhiko therefore became a boy with no friends, as we first see him in volume 1. In a new beginning, Kazuhiko begins making friends again in high school among people who never knew he was once a girl.

There are other effects too. Kazuhiko now has male equipment, but lacks male instincts, since his brain remains female. He copes somewhat by drawing on his/her LN knowledge, which helps him roleplay as a boy. Without male instincts, he sometimes guesses wrong.

So new Kazuhiko may actually be attracted to girls, or just roleplaying the way his LNs tell him he should.

This also raises the question of which characters know about his surgery. Kaju, Lemon, and Ayano, certainly. Nurse Konuki probably also knows. Anna and Komari probably don't know.