"In war there are no unwounded" soldiers. How is this quote related to the story?

Tim O'Brien's The Things They Carried speaks to both the physical and mental burdens carried by the men depicted in the collection of stories which make up the novel. Given that the men described carry both the seen and unseen, the quote in question parallels the novel perfectly.

In war, there are no unwounded soldiers.

The men in the collection of stories do carry physical items. They carry canteens, mosquito nets, guns, and ammunition. Yet, they carry some things which burden them far more. As told in the stories, many of the men carry guilt, fear, and the "what-ifs" of life. For example, Lieutenant Jimmy Cross carries a "what-if" regarding the woman he loves, Martha.
In regard to the quote, many of the soldiers carried wounds both seen and unseen. The physical wounds of a soldier tend to be apparent. Unfortunately, the unseen wounds tend not to be. Some soldiers returning from war carry with them guilt, anger, and traumatic memories which have the ability to continue to wound the soldier far beyond the physical wounds which heal. These wounds, sometimes being the reason behind PTSD (Post-Traumatic Stress Disorder), can impair a soldier's life to the point that he or she cannot function. Therefore, the statement in question offers readers an absolute regarding all soldiers returning from war: All soldiers are wounded in some way: emotionally, physically, or spiritually.