I'm still not sure about homelessness in particular, but the CDC, the New England Journal of Medicine, the Archives of Internal Medicine, and other scientific sources do suggest that combat veterans are at increased risk of various physical and mental pathologies and that combat veterans with PTSD are at higher risk still. A study in 2004 by Walter Reed Army Hospital concluded that approximately 15% to 17% of Iraq veterans could be affected by various mental illnesses.
If you're interested in more information of a scientific nature (rather than polemics from one side or the other), check out:
The prevalence of a history of post-traumatic stress disorder was 1 percent in the total population, about 3.5 percent in civilians exposed to physical attack and in Vietnam veterans who were not wounded, and 20 percent in veterans wounded in Vietnam....Although some symptoms of post-traumatic stress disorder, such as hyperalertness and sleep disturbances, occurred commonly in the general population, the full syndrome as defined by the Diagnostic and Statistical Manual of Mental Disorders, third edition, was common only among veterans wounded in Vietnam.This:
Design, Setting, and Participants Population-based descriptive study of all Army soldiers and Marines who completed the routine postdeployment health assessment between May 1, 2003, and April 30, 2004, on return from deployment to Operation Enduring Freedom in Afghanistan (n = 16 318), Operation Iraqi Freedom (n = 222 620), and other locations (n = 64 967)....
Results The prevalence of reporting a mental health problem was 19.1% among service members returning from Iraq compared with 11.3% after returning from Afghanistan and 8.5% after returning from other locations (P<.001)....Thirty-five percent of Iraq war veterans accessed mental health services in the year after returning home; 12% per year were diagnosed with a mental health problem....
Conclusions ...The high rate of using mental health services among Operation Iraqi Freedom veterans after deployment highlights challenges in ensuring that there are adequate resources to meet the mental health needs of returning veterans.
Adjusted attributable fraction estimates indicated that the following were significantly attributable to combat exposure: 27.8% of 12-month posttraumatic stress disorder, 7.4% of 12-month major depressive disorder, 8% of 12-month substance abuse disorder, 11.7% of 12-month job loss, 8.9% of current unemployment, 7.8% of current divorce or separation, and 21% of current spouse or partner abuse.Those interested in looking at this topic from a position that is skeptical of "the culture of victimhood," and who are interested in learning some fascinating history at the same time, could check out A War of Nerves : Soldiers and Psychiatrists in the Twentieth Century.