“Yes, but” - There's one important caveat: to make a definitive psychological diagnosis, you have to be able to examine someone. When it comes to the most psychologically complex accounts in ancient literature, we can't say that our accounts are entirely factual or some mixture of facts from different people with literary invention. So all we can say of ancient accounts is that some of the characters we find in literature behave much as we'd expect of someone suffering from PTSD
The Illiad in particular has been a source of endless commentary for depictions of what seem to modern eyes to be PTSD in soldiers. The most well known example of the literature would be Jonathan Shay's Achilles in Vietnam: Combat Trauma and the Undoing of Character.
Shay is an MD PhD clinical psychiatrist, who says directly: "Homer's Iliad (Homer, 1975/ca. 800 B.C.E.) remains an outstanding narrative of toxic combat experiences that appear similar to those reported by Vietnam Veterans with severe, chronic post-traumatic stress disorder (PTSD).
There was a recent attempt to connect contemporary veterans with the classical antecedents: "These Are Men Whose Minds the Dead Have Ravished": "Theater of War / The Philoctetes Project"; and contemporary veterans do see parallels in some of the ancient stories.
But caution has to be exercised. For many years it was a commonplace to explain the retirement of the Holy Roman Emperor Charles V as exhaustion and depression from war. More recently, physicians and chemists were able to examine the remains of the long dead Emperor, and found that he was suffering from terrible gout at the end of his life; that physical pain is likely what caused his "depression" and retirement to seclusion in the monastery at Yuste.
So, yes, there's every reason to believe that ancient soldiers suffered from battlefield trauma, particularly due to the intimate nature of the violence, but care should be taken not to be too bold. Reading the past for personality is challenging, the cues and and responses we take for granted when evaluating a living person today are a matter of inference in historical accounts.
Sources
Learning about combat stress from Homer's Iliad
Achilles in Vietnam: Combat Trauma and the Undoing of Character.
"These Are Men Whose Minds the Dead Have Ravished": "Theater of War / The Philoctetes Project"
Not to discourage other people offering from offering answers, but this older post by u/hillsonghood discusses this issue and its complications extensively.