I've seen it many times, especially during lunch. Both men and women. It may not be often or common practice, but, if people can bury their faces in their phones 80 hours a day, I see no problem with reading an actual book and having a drink. Go ahead..
I wouldn't be able to read at a bar that's crowded with loud music playing, it would be too distracting. But that's me. If you're able to do it with getting distracted, that's cool.