It is possible for parts of the brain to be asleep while others are awake. It can also be possible for the brain to show awake patterns mixed with delta for short bursts. This can happen for instance because of severe sleep deprivation, lesions or epilepsy. The whole brain simply cannot be in constant delta wave and the patient being awake. It is simply impossible. If this was the case I'd think the EEG needed to be repeated because it then seems like glitchy machinery.