What a great question! My answer is yes and no. Let me explain. Firstly, there are some important indications in the text that point towards the massive mental instability of Holden as a result of what he has gone through with his brother's death. Note, for example, what Holden tells us about Allie and how he responded in Chapter Five:
I was only thirteen, and they were going to have me psychoanalysed and all, because I broke all the windows to the garage. I don't blame them. I really don't. I slept in the garage the night he died, and I broke all the goddam windows with my first, just for the hell of it. I even tried to break all the windows on the stations wagon we had that summer, but my hand was already broken and everything by that time, and I couldn't do it.
Such offhand descriptions of what must have obviously been a very difficult time in Holden's life point towards massive unresolved issues of grief and acceptance of his brother's death, which if we psychoanalyse, can lead us to suggest that Holden's breakdown that he experiences in this novel is partly the result of such unresolved issues.
However, on the other hand, looking at this question from a novel perspective, what depresses Holden and upsets him greatly is the "phoniness" that he sees all around him and displayed by everyone in society, even those he trusts most. When we consider this for one moment, we can see that he has a point. Certainly for an idealist like Holden, he sees attributes and characteristics even in those in whom he trusts that causes him to question the world. Consider Mr. Antolini, a favourite teacher of Holden, who abuses that trust by making a pass at him. The world is shown to be lacking in the basic moral principles that Holden holds in high importance. Therefore, to a certain extent, we can also argue that he is the only sane person living in a sane world.