Almost always, yes. Sometimes I leave it in because how it's said is funny/hot/whatever. I think it's happened once or twice by accident from other studios. I recall Paradise Vision left it in a clip way back in the day, either deliberately or not.
I did once have a model (Macy Divine) tell me "just because I use my safe word, doesn't mean you have to stop." I told her my lawyers felt otherwise. She then clarified, "No, I mean just switch spots." I was still like, no.
If you ever run across a producer who neither uses nor respects safewords, RUN.
As an aside, OP, this is like the third time you've implied that producers force models to put up with shit they don't want done. There's a lot I could say about that, but I'm biting my tongue.
The dozen of models that I've played with have all had a safe word and I've been very proud when I've gotten some of them to use it! It doesn't matter whether your playing with a model or non model you should always use a safe word and put the safety and comfort of your partner above all else!