I guess the simple answer to that is "NO".
However, the accepted theory does seems to be that creative people are much more prone to depression, anxiety & other forms of mental illness.
So...based on what I've read, personal experience & what I've heard from people inside the industry, I'd have to say that we're sad more often than most.
Some years back, I was on the mailing lists of a few small & mid-level publishers. Two of them sent out regular newsletters, as well as issuing call-outs for specific projects. One of those newsletters, from a publisher in California, talked extensively about how commonplace depression was in the songwriting community at large. The open, casual way in which he discussed it, left me with the distinct impression that within the larger music industry, the link between the two was common knowledge.
I quickly Googled the topic & pasted in a variety of article links below. If you're interested, I'd suggest Googling it yourself. You'll get hundreds, if not thousands of pertinent links, articles & discussion boards.
I recognized early on that musicians & writers were different. Not worse, not better, simply different!
If I'm being completely honest, that difference was a big part of what drew me in. For me, it was part of the mystique.
I've wanted to be many things in my life, but the one thing I've NEVER wanted to be was "just like everybody else".
As long as they aren't disruptive to my overall exisitence, I try to embrace my differences...always have.