It happens. In my 20 years book retail experience, I’ve seen about a dozen copies we knew about (it’s faulty, and thus can be returned or exchanged) out of thousands of books handled. Bear in mind most books aren’t even opened until they are bought and read. Yours will be more valuable for the signature, arguably less so for being faulty, but I don’t think that’s an issue, as long as you list it, to avoid complaints. Technically you’d be listing it as ‘imperfect’.

HTH