As John Nash was a real person who actually suffered from schizophrenia, I searched to see if his real desk had ever been thrown from a window. I did not find a definitive answer, but it appears unlikely.
According to one comparison of the film versus the biography on which it was based, in real life, Nash did not hallucinate a roommate. There are also apparently many other differences between the story in the film and the real life of Nash, both in relation to his illness and other details.
With that out of the way, I think it helps to see the entire scene, which doesn't start up in the room/office with the desk, it starts with the conversation with Helinger (Judd Hirsch). Helinger essentially tells Nash that Nash isn't good enough. After which Nash returns to his room/office angry and frustrated. He hallucinates Charles, and has a violent argument with him. We see Charles push the desk over and through the window, and two students walking in the quad outside stop and stare in shock.
Without any clarification from the filmmakers, the most likely interpretation of the story is that what "really" happened is Nash did push his desk out of the window himself because of his rage and frustration, and hallucinated that Charles did it as part of his illness and also as a rationalization. We are shown this scene in this way so we get a sense of Nash's drive, passion, determination, and also erratic nature. And yes we are meant to be kept comfortable with Charles being "real".
I couldn't find any information on whether people suffering from hallucinations in the real world blame their own actions on their hallucinations, but it happens all the time in film and TV shows.
In summary, we are meant to think that Nash himself pushed the desk through the window, the two students outside are real and shocked, and Nash believes it was Charles who pushed the desk out.