All the time in middle school and high school, I’ve heard, for example, “My girlfriend doesn’t like that I do X” or “My wife and I did X this weekend”, and since the teacher is a man, it’s seen as acceptable.
Would casually mentioning having a girlfriend cause angry emails from parents, even if I’m not discussing forms of romantic attraction in schools? These kids are like 11-14 anyway, parents’ job to teach orientation (which I’ve heard argued) or not.
Also, we learn relationship descriptions in middle school Spanish if you choose to take it, which includes words like novio, novia, esposo, and esposa. (Shouldn’t matter, especially if the school I teach in is at a non-Conservative community)
I guess it depends on how much you need to keep that job or career path.
Can you? Definitely. But where you are based, that choice might have very long term consequences for your career.
If you intend to continue your lifestyle as a teacher… Yo que tú no lo haría.