I don't think they really give a shit either way. They have a certain order for mandatory OT based on seniority and when the last time you got mandated was. I don't think it matters if you volunteer every day for a week, if it's your "turn" and you don't volunteer and they need the people, they will mandate you.
Some of the managers are way better at getting volunteers than others. There's a number people can call to come in on their off day/before their assigned shift or whatever, and I've heard that some managers don't even bother to check who called it. So there are people willing to come in but people still get mandated.