The cause of suspension trauma isn't fully known but is thought to be due to a lack of returning blood from the lower limbs. It is known that hanging immobile in a vertical position can lead to Suspension Trauma and this can happen surprisingly quickly as has happened when investigating the problem in France: Proposal of an Effective Algorithm to Manage Suspension Trauma in the Field.
In 1973, Amphoux performed a short series of suspension tests, which ended rapidly due to all subjects almost reaching the point of unconsciousness with disturbing hemodynamic data. In 1979, the medical commission of the French Federation of Speleology studied reports of 15 unexplained deaths among trained cavers during rope ascents. They first thought that the cause of the death was hypothermia, yet as they examined each case, they realized that the delay before loss of consciousness was too short to be compatible with hypothermia. These data where mentioned in 1992 in an article of Bariod who performed tests on healthy volunteers wearing a caving harness.
This study conducted under medical supervision and monitoring, was quickly stopped due to the occurrence of phases of severe bradycardia with loss of consciousness in two subjects after 7 minutes of suspension for the first and 30 minutes for the second. The experiment was repeated two years later in three healthy volunteers but was ended equally abruptly following the occurrence of severe malaises including a loss of consciousness. These two studies, although aborted, ruled out the possibility of hypothermia as the key role in the deaths, as had originally been thought.
As stated in the Wikipedia article referenced in the question: Suspension Trauma:
Suspension trauma (Syn. "orthostatic shock while suspended"), also known as harness hang syndrome (HHS), suspension syndrome, or orthostatic intolerance, is an effect which occurs when the human body is held upright without any movement for a period of time. If the person is strapped into a harness or tied to an upright object they will eventually suffer the central ischaemic response (commonly known as fainting). Fainting while remaining vertical increases the risk of death from cerebral hypoxia. Since there is no evidence that these effects are specifically due to trauma, or caused by the harness itself, climbing medicine authorities have argued against the terminology of suspension trauma or harness hang syndrome and instead termed this simply "suspension syndrome".
People at risk of suspension trauma include people using industrial harnesses (fall arrest systems, abseiling systems, confined space systems), people using harnesses for sporting purposes (caving, climbing, parachuting, etc.), stunt performers, circus performers, and occupations that require the use of harnesses and suspension systems in general. Suspension shock can also occur in medical environments, for similar reasons.
So a full body harness would not make any difference as this is what is used anyway in industrial applications and Suspension Syndrome is known to have occurred in such situations as well.