From looking at the context, he was alive enough to pray.
Jon 2:1 Then Jonah prayed to the LORD his God from the stomach of the fish, 2 and he said, "I called out of my distress to the LORD, And He answered me. I cried for help from the depth of Sheol; You heard my voice. 3 "For You had cast me into the deep, Into the heart of the seas, And the current engulfed me. All Your breakers and billows passed over me. 4 "So I said, 'I have been expelled from Your sight. Nevertheless I will look again toward Your holy temple.' 5 "Water encompassed me to the point of death. The great deep engulfed me, Weeds were wrapped around my head. 6 "I descended to the roots of the mountains. The earth with its bars was around me forever, But You have brought up my life from the pit, O LORD my God. 7 "While I was fainting away, I remembered the LORD, And my prayer came to You, Into Your holy temple.
Seems to be quite a bit of figurative language. I am sure the experience was "hell" but from what I see from the wording he was alive enough to pray. Not sure I can be animate about it but the awareness he had of his experience and the still praying part leads me to believe that he was alive and never died, unless there is another verse somewhere.
It's certainly not necessary for him to die for the analogy to work. Three days and three nights in the fish, three days and three nights in the earth/tomb. Just asking, by the way. It's the only way to learn.
