Does breathing have anything to do with energy orgasms?

Yes and no. Some utilises breathing to help activate the orgasmic expansion. But it's not necessary. Breath like other methods can amplify our lifeforce within. And by the breath alone we can become pretty ecstatic.

Can everybody become orgasmic?

To what I have seen so far, yes. And so I believe. It's all about body dynamics, for some it might require a bit more practice/preparation than others. But so far, i haven't seen anyone who wasn't capable of becoming energy orgasmic. That also counts women who never had a physical orgasm before.