According to Chalcedonian Trinitarians, did Thomas - a devout Jew - believe God had died at John 20?

At John 20, Thomas initially refuses to believe other disciples' accounts of Jesus having been raised from the dead. When Jesus appears to Thomas, Thomas famously exclaims > "My Lord and my God!" Do Chalcedonian Trinitarians who believe Thomas was claiming Jesus = God here, also believe that Thomas would have held therefore that God could have and had died?