When duplicate questions are closed, they are not deleted. This is a deliberate feature—by closing duplicates but leaving them to remain on the site:
- There is only one canonical question where all the answers are posted, but...
- Users coming in from Google will still find the duplicate question if they search for that wording.
If a duplicate question has answers, they still remain on the duplicate, and a link to the open master question is placed in a banner. If the duplicate is closed before being answered, users coming in from Google will automatically be redirected to the answered master question.
In answer to your question: yes, the duplicate should be closed, because it will still stay on the site as a 'signpost' for other users searching for an answer, but having only one canonical question prevents good answers being spread among many duplicates.