Currently, if you go into the communication section of a contact in the mobile app, there is an option for you to add an internal comment. However, if there is no conversation activity (such as an email, SMS, or an internal comment from the desktop app), then the option to add the internal comment on mobile does not appear. Meaning, if somebody creates a contact from the mobile app, they have to wait for somebody else to post a comment from the desktop app to add their own internal comment.
This option to add an internal comment should appear always, even if there is no conversation activity yet.