If you know how to train a parrot, then yes, a "one person bird" that "prefers one sex" can be taught to go to anyone.
My mitred conure is supposedly a one person bird who prefers men, after all, he was owned by one man for 10 years of his life. Charlie lived in a pet store for about a year where he did bond with a young girl, then in a foster home for a year where he bonded with both humans. He's now been with me for 6 years (making him 18, going on 19). I'm most definitely not male, and he's quite bonded to me! I can't say I've noticed him to prefer one sex over another, nor have I noticed him to be a 'one person bird' - he simply doesn't like strangers all that much! He takes a while to warm up to new people, and it's a matter of people frequently interacting with him over a few weeks. If he doesn't like someone, he wont take food from them, even if it's the same thing I'm eating, and because I'm eating it, he wants some. (he always wants what I'm eating! even if he doesn't like it! LOL) However, people he does like, he will take food from willingly. He may not care what they are eating, but if he is offered it, he will take it and eat it.