He is seen and only appears in the mission Shore Leave, which was previewed during the EAs showcasing during E3.
Sgt. Wright is modeled after real Marine Sgt. Drew Wright who developed Ewings Sarcoma after his initial enlistment which included a tour to Iraq in 2008 in support of Operation Enduring Freedom as Military Police. He lost his fight with cancer at the age of 25.
After the mission, he doesn't appear again in the game.