That's irrelevant. They still get a notification to disturb them, they still can see it when looking at their phone, they can still be concerned about the content and how to respond later even if they don't answer, they can still be concerned about the content even if they don't read it, they could very well be waiting an important message at the time, they might have an experience with other people/ex-partners/etc pressuring them to answer immediately, and so on.
Technical terms like "asynchronous" don't mean anything to how people use a technology. Common social expectations do.