Is it rape if it's just verbal coercion?

A friend shared with me that one night, she was alone with this guy. They were friends. And they were joking about how they were going to have sex and so on. But then when they "got down to it," she said no, that they didn't have any protection, and didn't want to. He kept trying to convince her and kept saying yes, let's do it, and so on, while she kept saying no. She didn't push him away or anything, she just kept saying stuff like "No, we can't, we shouldn't, not now." Finally he just...did it anyway. Would you consider this situation rape? She is unsure what to do now.