No, that is not the case either. When an atheist, for example, reasons that there is no God because there is a natural way for the universe to form itself, that is use of reason, despite the error in the conclusion.
Simply because Hawking is known to be highly intelligent doesn’t mean he’s right when he says the universe “can and will create itself,”
The statement is a good example of logical incoherence, or unreason. A thing cannot precede itself, therefore it cannot create itself.