autoreply on noreply address

Let's suppose a website that sends (useful) mails from a "noreply address". Nobody read messages from this mailbox because it is just to notify (useful) information.

At this time, if someone, sends an email to noreply the silence is the answer.

But, here, they are a person with a great idea: set an autoanswer on noreply mailbox to reply people with a message "this is a noreply address, no body read this message, thanks".

In my opinion this is a kind of oxymoron, an autoreply on a non-reply mailbox. But, may be, this is a bad pattern in other effects that I can't see at this moment or may be this is a good solution to let know people don't wait for a reply.

Question:

In terms of user experience, is a good idea to configure an autoreply on a non-reply mailbox to say people nobody is reading their mails?

Notice: ( Edited due Pectoralis Major's answer )

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