If you send a Message to another member while your profile is Hidden, that member will receive your Message as normal. They will be able to read your Messages, but they won't be able to view your profile page. Instead, they’ll see a notification that your profile is unavailable.
While your profile is Hidden, you probably won’t receive a lot of new Messages, because you won’t be appearing in other members’ search results or matches. You may still receive Messages from members you have already contacted. They can’t view your profile, but your previous Messages will still be in their Inbox, so they can reply to those Messages.