Nope! Not in the USA, anyhow. If you sue without registering, all it does is make statutory damages unavailable, it doesn't block you from filling suit. Also, you can register any time before filing suit, losing only your presumption of validity in certain cases. That said, both of those things are highly desirable, so it would be pretty silly to sue without taking care of those matters first.
That said, get a lawyer if you ever have more than an academic interest in this, because there are always weird edge cases when dealing with the law.
...the Copyright Office must have acted on your application
before you can file a suit for copyright infringement, and certain remedies, such as statutory damages and attorney’s fees, are available only for acts of infringement that occurred after the effective date of registration.
A patent must be filed & public to be granted.
A copyright must be registered to file suit.
To allow destruction would violate the very purpose of patent/copyright.