Answer transcribed from Brightway's interview with Dr. Thomas Franz:

In more severe brain injuries, features that look very much like psychiatric disorders, such as a bipolar affective disorder with manic episodes, can look like psychosis. However, not so much with post-concussion syndrome. That really is a lesser type of brain injury. It has its own sometimes very difficult functional deficits but in terms of the actual injury to the brain, it should not be severe enough to cause psychosis. 

Now, if a person is developing what is called now chronic traumatic encephalopathy, which is the result of years of repetitive concussions, then yes psychotic or major depressive features, or dementia can easily be present. However, that's not a single injury with a post-concussion syndrome, that's a cumulative effect of many head injuries.