I'm sure it would.

As usual in these matters if someone resigns/tells you they don't want to work for you any more, and they won't put it in writing, there isn't much you can do about it really - is there?

Hi Luis,
Although a letter would be ideal to have on the files, an email should suffice too. In my experience, many resignations in Germany happen in face-to-face meetings with line managers without any written statements from the an employee's side at all, so it is up to the Company to follow up with a written confirmation of resignation or similar statement.

Best Regards,
Anna