Will sending a copy of the sick certificate be recommended?

It depends on which process or for which legal relationship you need to confirm the fact of receipt of the document.

Generally, sending a document by registered mail with return receipt to the correct mailing address is considered a proper way to prove mailing and delivery. The return receipt confirms that the addressee received the letter, or (if the addressee refused to accept it or did not show up for it) that the letter was properly sent.