Does medicine only work if the patient fully understands what it is and how it works? Do doctors need to provide their patients an education in chemistry and a pharmacy before adminstering drugs? The medicine, administered properly is good for the sick patient. It matters not what the patient understands of the medicine.
The Body and Blood are good and nourishing to the faithful. Does that change if the partaker does not fully understand its significance? Does anyone really fully understand this sacrament?
In the Eastern Churches, the sacraments are referred to as the Holy Mysteries because, as you pointed out, it is a mystery as to how it works.