Is it possible for a brain hemorrhage to be detected through an ophthalmological exam?

Yes: The covering around the optic nerve is the extension of one of the coverings around the brain (arachnoid mater) a sub arachnoid hemorrhage may be detected by the ophthalmoscope.

Brain hemorrhage: Yes. There is a syndrome called terson syndrome where a type of brain bleed called a subarachnoid hemorrhage occurs in conjunction with retinal and vitreous hemorrhage. Also, if a brain bleed leads to elevated intracranial pressure this can lead to optic nerve swelling (papilledema) which can be detected on an eye exam.

Yes: Yes you can see swelling in optic nerves if there is pressure in the brain. You can sometimes see visual field defects on visual field testing if the hemorrhage is in the visual part of the brain.