Thing is with the fragments passing through clothes dragging fibres into the wound and stuff going into his intestines would cause bacteria to run rampant through his system plus they only really started using penicillin in 1942 who knows gas gangerene etc.
From WIKI: "A Czechwoman went to Heydrich's aid and flagged down a delivery van. He was placed on his stomach in the back of the van and taken to the emergency room at Bulovka Hospital. He had suffered severe injuries to his left side, with major damage to his diaphragm, spleen, and one lung. A splenectomy was performed, and the chest wound, left lung, and diaphragm were all debrided. Himmler ordered Karl Gebhardt to fly to Prague to assume care. Despite a fever, Heydrich's recovery appeared to progress well. Hitler's personal doctor Theodor Morell suggested the use of the new antibacterial drug sulfonamide, but Gebhardt thought that Heydrich would recover and declined the suggestion. Heydrich reconciled himself to his fate on 2 June, during a visit by Himmler, by reciting one of his father's operas: The world is just a barrel-organ which the Lord God turns Himself. We all have to dance to the tune which is already on the drum.
Heydrich slipped into a coma after Himmler's visit and never regained consciousness. He died on 4 June; an autopsy concluded that he died of sepsis.