Yes, I will absolutely eat something I don't like if it is served to me. I also make and eat things I don't like. Salmon, for instance. The kids enjoy salmon, so I'll serve it on occasion. The 10 year old doesn't care for asparagus (though she likes it more, recently) so that gets served less frequently than other vegetables, too.
I will eat Brussels sprouts in any way, but the kids have preferred preparation methods - sautéed or roasted - so we tend to prepare them that way, rather than a less preferred method.
I hated squash as a child, but learned to prepare squashes in ways I love as an adult.
Very few things are off the menu here.