YES if the q-banning formula guessed by people is on the right direction.
I think Shog9 is authoritative as a a former employee. Shog9 says that, a well-received but closed question is probably positive and possibly non-positive. To my knowledge, a well-received but open question is certainly positive (correct me if I am wrong). Therefore, the action of closing an earlier question still penalizes the asker.
For example, a well-received open question worth two dollars, and a well-received closed question worth one dollar. This means that "well-received" equals two dollars and the action of closing or marking as duplicate always means negative one dollar.
By the way, the OP of this post was asking if the action of "marking as duplicate" or closure due to duplication is negative or positive. Some other answerer are saying that some closed questions are positive. I do agree with their point, but they do not directly answer OP's question.
Another user ᔕᖺᘎᕊ also confirmed that duplicates are counted in the auto-ban formula. He also confirms that closing, duplications, and downvotes are treated similarly in the system.
PS: I don't know why reasonable doubts against this site are usually suppressed. Here are some common Q/A for this answer:
- "But Shog9 did not say that a well-received but closed question is possibly non-positive".
Fact: Shog9 clearly said that "a well-received but closed question is probably positive". It is common knowledge that "probably" means "above 50%".
- "I agree that a well-received closed questions worth less than a well-received open question. But the question still has positive weight and closing question does not harm the asker."
Fact: for example, if a well-received open question worth two points, a well-received closed question worth one point, then closing a question means -1 point: a one point harm done on the asker. The OP is asking about the action of "marking an earlier question as duplicate".