Can the extent of a neurological injury that a patient may have sustained be determined while the patient is unconscious? comprehensive answers are very much welcome?

Yes, an experienced neurologist with the help of advanced neurodiagnostic studies (CT, MRI, ECG, etc) can predict the prognosis when patient is in coma and this situation is commonly seen in traumatic brain-spine injury, a catastrophic intracerebral bleeding subarachnoid hemorrhage, etc.

The anatomical extent of a brain injury can be visualized on an MRI study, and physiological function can be objectified on a bedside EEG. The neurological exam can determine the brainstem level present secondary to the coma. More extensive and precise details are present in the classic book, "Stupor and Coma" by Plum and Posner.