Heraclius could have died in several ways even after he reached Constantinople. He had several close shaves in battles against Shahrbaraz's and Shahin's armies, particularly when Shahrbaraz ambushed him. Any lucky shot could have killed him and that would be the end of the Byzantine effort.
Actually, I'm wondering if no Heraclius would make things better for Byzantines. IIRC, before the deposal of Phocas Persians only took a few border fortresses. Only after the revolt of Heracliuses Persians really started to gain territory.