As a starting point, PTSD around the time of WWI was often lumped with "shell shock." This 1922 British publication reveals a struggle in the medical profession to delineate "shell shock"—complications resulting from the concussive effects of explosions—from "war neurosis" (pp. 4-6). This might be helpful in searching for other primary sources pertaining to WWI and WWII veteran suicides.

EDIT: as /u/Romiress points out, the next article I look at might be crap. I am keeping it up because it seems to use a few decent sources that might serve as a starting point for anyone who has time to look into this further. My apologies.

This article contains graphs of Canadian male suicides by age and military service. I do not have the time to verify its information, but it shows a marked increase.

I would follow that article's chain of references to verify its legitimacy, but it appears that the answer for WWI is yes, post-war veteran suicides were a major problem.

EDIT 2: The more I read about suicide from an historical context, I get the sense that it is a complicated (but not impossible) problem to approach from an historical perspective. Statistics on suicide are shaky due to the social stigmas surrounding suicide and the ambiguity of circumstances surrounding suicidal and accidental deaths. The best article I read on the subject of studying suicide from an historical perspective is Dr. Roisin Healy's "Suicide in Early Modern and Modern Europe" (The Historical Journal 49 no. 3, 2006. pp 903-19).

I did find a NY Times article dated June 2, 1922, "VETERANS' SUICIDES AVERAGE TWO A DAY: Legion Official Declares Worst Casualties of World War Are Just Appearing." It mentions the 1922 Second Deficiency Appropriations (Langley) Bill, part of which allotted a significant sum of money to bolster military medical facilities dealing with psychiatric and Tuberculosis patients. The article focuses on the claims of a C. J. Harris, an official of the American Legion in Indianapolis, so it is probably very biased. Still, it shows that veteran suicide was a public concern in 1922.