Apparently, it is. An article in The Australian indicates that it is a real issue.
"This war has made a lot of youth angry ... It has made a lot of people challenge things which they thought were basic, like Australia was a good guy, Australians were never aggressors in war, that we were a humanitarian country."
This is hardly a problem restricted just to Australia -- it is a global issue. There are over 30,000 suicides a year in the US alone, so it is entirely possible that the war could contribute to that number significantly. People will, in effect, be dying for the war on the homefront.
I did find one statistic that was interesting -- the suicide rate went up 14.4% during the Vietnam War era. That era, incidentally, had the highest recorded rate of suicides in US history. If you assume 30,000 suicides a year in the US, and if the war lasted three months and increased the suicide rate similarly, this would mean that the war caused an additional 1050 suicides.
Of course, those figures could be way too high -- there were other reasons why the suicide rate increased during the Vietnam War. However, we know that there is a direct link between post traumatic stress disorder and suicides. We've seen this in Vietnam, The Falklands, etc. In short, suicides are a significant, if underreported, additional cost to the war.
Of course, the feelings of anger, pain, and powerlessness are even greater in the Arab world. Do we really want a bunch of potentially suicidal Arabs right now?