Yes, the "possible duplicate" block is edited into the question by the Community userCommunity user upon closing. It will not be automatically removed when the question is re-opened. Someone else (either the original asker, or the person who casts the last re-open vote) will have to edit it out manually if they want it gone.
I usually leave it there... It says "possible duplicate", not "exact duplicate", so the information it contains is still potentially relevant. But feel free to remove it from questions where you don't think it applies.