I can't find a clear argument from data to dispute what your point, which is good and very plausible, but I also can't find one to substantiate it. What I can say is that most likely homeless women are subject at higher rates to the types of assaults that are more likely to cause PTSD, presumably this would also include transgender MtF and similar groups. For male homeless people the data does not substantiate high enough rates of being exposed the the types of experiences more likely to cause PTSD.

However, female and intersex/trans people are a very small percent of the homeless population. So while PTSD is statistically plausible within that sub-group, we are now taking a moderate percentage that would get PTSD from exposure to a potentially triggering event (say 15%), with a small percentage exposed to that event, among a very small percent of homeless people overall. Just giving this the highest numbers I can substantiate in your favor, it would produce 1.2% to 1.5% of the overall homeless population developing PTSD from triggers that are statistically due to homelessness PER YEAR (aka you can be raped if you have a home, but you are more likely to be raped if you do not have a home). This would accumulate to 4-6% out of about 25-50% prevalence of the PTSD cases found in homeless people. This is significant, so your theory is plausible given the available data.

However it would still mean that PTSD is 5-10 times more likely to cause homelessness, overwhelmingly due it's contribution to rates of hard drug addiction, than it is to be caused BY homelessness.