"Can A Herniated Disc In The Neck Cause Paralysis?"
by Dr. Benjamin Geddes

It's possible if you, you know, depending on the location, again, more typically the herniation is what we call paracentral, meaning that they come off more to the side and that pinches the nerve coming off of the spine. It is possible, particularly if you had a trauma or something acutely, where you had a large disc herniation that was central. It is possible that you have, again, that cervical myelopathy situation where you have compression of the spinal cord.

And theoretically, if you had enough compression and particularly over a really acute period, you could get enough swelling in the spinal cord to have really significant neurologic problems.