Probably...
The figurative death position would make sense
if Jonah had praised God for bringing up his life from the pit after God had brought Jonah up out of the fish and out of the sea. Instead he praised God for bringing his life up from the pit before God had brought him up from the sea.
6 To the roots of the mountains
I went down to the land
whose bars closed upon me forever;
yet you brought up my life from the pit,
O Lord my God. - Jonah 2:6
Only after he thanks God for raising up his life does the fish spit him out.
10 And the Lord spoke to the fish, and it vomited Jonah out upon the dry land. -Jonah 2:10
If death was just a figure for being in the fish, it makes no sense for Jonah to praise God for bringing up Jonah's life from the pit, when Jonah's life was still in the fish. Nothing would have actually changed since he was in the fish for three days.
In Jonah's prayer he descibes:
The waves and the billows passing over him, being surounded by the deep, having weeds, wrapped around his head, his life fainting away as he calls out to God, and being in the belly of Sheol, under the roots of mountains were the bars closed upon him forever... but he makes no mention of being swallowed by a fish or even of any awareness that he is actually in a fish.
This indicates that Jonah's last moments of conscious awareness all occurred while Jonah was outside the fish before God appointed the fish to swallow him. This makes it much more likely that Jonah was actually unconscious and even dead, having drowned, before his body was stored within the fish for a time period spanning three days and three nights. It seems, otherwise, he likely would have mentioned something about hanging out in the fish he was picked up in since he was so conscious and descriptive of everything else.
Looking at it another way in relation to the Activity of God,
There were only two acts that the scriptures actualy claim that God performed after Jonah was swallowed:
- Bringing up Jonah's life from the pit -Jonah 2:6
- Commanding the fish to vomit up Jonah onto dry land - Jonah 2:10
The two actions of God, resurrecting Jonah & vomiting him from the fish, are chronologically separate events and are not the same event, as those of the physical death camp often assert. The 'resurrection happened in the fish and not out of the fish. Then Jonah was vomited up.
There is no mention of God preserving Jonah's life for three days & three nights in the belly of a fish, which would have been a third act of God as any thinking person would acknowledge. This third act would necessarily be read into the text by the figurative death camp, since it is nowhere present in the text itself.
Lastly,
Now, of course, understanding that Jonah literally died and was brought back to life strengthens the meaning of his connection to Jesus:
40 For just as Jonah was three days and three nights in the belly of the great fish, so will the Son of Man be three days and three nights in the heart of the earth. -Matthew 12:40
That said, this is not a deciding factor for me. I was previously comfortable with the connection Jesus made here even if Jonah's death was not literal. It just makes much more sense now I know that it is literal.
So, with these fact patterns, when Jonah praises God for bringing up his life from the pit, Jonah was actually resurrected after 3 days and three nights in the fish. Jonah was actually greatful to be found alive when he certainly died despite the likely discomfort of being stuck in the middle of a fish in the middle of the sea.
Note regarding David and Sheol:
In Psalms, David only describes being surrounded by the threat of Sheol or being saved from Sheol. David never actually locates himself as being formerly in Sheol the way Jonah did in his prayer to God.