a song of ice and fire - Is Quentyn Martell the Sun that rises in the west and sets in the east?

One of the main plots of Dance of Dragons is

The travel of Quentyn Martell to meet Daenerys Targaryen with the objective of setting up an alliance and, maybe, establishing it by marriage. Sadly, his journey is suddenly stopped when one of Daenerys' dragons burns him to ashes.

Well, after reading the book it felt quite strange for me that Martin had dedicated so many book pages to a story, apparently, without real impact on the big picture.

But speaking of it recently with my girlfriend (who is quite a visionary I must say), she stated that the reason is that Quentyn's story is one narrative arc that fulfills one of the Mirri Maz Duur's prophecy about the future children of Daenerys, the part that states "When the sun rises in the west and sets in the east".

I was quite shocked by the revelation, as to my understanding it fits quite well on the prophecy and explains why so many pages to start and end an inoffensive story arc, but I wonder if there is some other clue or point in the novels that can confirm this theory.

Answer

As per the Fan theory your Girlfriend is referring to, yes, Quentyn is the sun which set in the East.

Mirri's prophecy was:

"When will he [Drogo] be as he was?" Dany demanded. "When the sun rises in the west and sets in the east," said Mirri Maz Duur, "When the seas go dry and the mountains blow in the wind like leaves. When your womb quickens again, and you bear a living child. Then he will return, and not before."

_{AGOT - Daenerys IX}

So for Drogo to return:

1. Sun has to rise in the West and set in the East.


2. Seas have to go dry


3. Mountains have to blow in the wind


4. Daenerys has to give birth to a living child

The fan theory is, that the prophecy has been fulfilled for following reasons.

When the Sun rises in the West and sets in the East

Quentyn Martell belongs to House Martell whose sigil is Sun pierced by a spear. He was born in Dorne, Westeros and died in Meereen, Essos. So The Sun rose in the West and set in the East.

From the Citadel:

Consider that Quentyn Martell -- "the Sun's son", referring to the Martell sun -- journeyed from the west to the east, where he died

When the Seas go dry

The Sea that went dry was the Dothraki sea. Daenerys noted that the grass of the Dothraki sea had gone dry.

From the Citadel:

In Daenerys's last chapter she notes that the Dothraki sea is going dry and the grasses are dying

And also:

Dany set off through the tall grass at a brisk pace. The earth felt warm between her toes. The grass was as tall as she was. It never seemed so high when I was mounted on my silver, riding beside my sun-and-stars at the head of his khalasar. As she walked, she tapped her thigh with the pitmaster's whip. That, and the rags on her back, were all she had taken from Meereen.

Though she walked through a green kingdom, it was not the deep rich green of summer. Even here autumn made its presence felt, and winter would not be far behind. The grass was paler than she remembered, a wan and sickly green on the verge of going yellow. After that would come brown. The grass was dying.
_{ADWD - Daenerys X}

And:

The next morning she woke stiff and sore and aching, with ants crawling on her arms and legs and face. When she realized what they were, she kicked aside the stalks of dry brown grass that had served as her bed and blanket and struggled to her feet.
_{ADWD - Daenerys X}

And mountains blow in the wind like leaves

The mountains that blew like leaves are the tricky part.

From the Citadel:

Two of the pyramids of Meereen collapse in smoke and ash following Viserion and Rhaegel rampaging through the city and that she menstruates

But from a fan theory:

Now the most confusing aspect of the prophesy (my theory for which is kinda tinfoily so bear with me). ‘The mountains blow in the wind like leaves’ does not refer to the destruction of Meeren or any form of volcanic eruption but to Ser Robert Strong. It is widely believed that Ser Robert Strong is Gregor Clegane (aka the mountain)’s reanimated corpse. It is however noted that Gregor's head was shipped to Dorne. This decapitation would mean that the one “mountain” has now become two “mountains”.

I'd like to add that since Mountain's body is in King's Landing and his head is in Dorne, One could say that of the two Mountains, one has blown like leaves to Dorne. Citadel however points to destruction of Pyramids.

An alternative view is the one suggested by Joao Duarte in the comments, If somehow the Wall is brought down, it could also be something akin to Mountains blowing in the wind like leaves.

OMG IF DANY CAN HAVE BABIES THEN DROGO WILL RETURN?

We must note what the Citadel says:

This might be a real prophecy, or it may simply be a sort of curse to strike terror and despair into Daenerys's heart.

And also:

This of course leaves us the need for a living child, and then the "return" of Drogo... though our speculation is that if she has a child, it will be a son that she names Drogo, thereby fulfilling Mirri's claim.

There is also speculation that Daenerys bleeds (Menstruate) for the first time in months when she is lost in the Dothraki sea, Which means she may have miscarried a child.

Just past midday she came upon a bush growing by the stream, its twisted limbs covered with hard green berries. Dany squinted at them suspiciously, then plucked one from a branch and nibbled at it. Its flesh was tart and chewy, with a bitter aftertaste that seemed familiar to her. "In the khalasar, they used berries like these to flavor roasts," she decided. Saying it aloud made her more certain of it. Her belly rumbled, and Dany found herself picking berries with both hands and tossing them into her mouth.
_{ADWD - Daenerys X}

And:

When she woke, gasping, her thighs were slick with blood.

For a moment she did not realize what it was. The world had just begun to lighten, and the tall grass rustled softly in the wind. No, please, let me sleep some more. I'm so tired. She tried to burrow back beneath the pile of grass she had torn up when she went to sleep. Some of the stalks felt wet. Had it rained again? She sat up, afraid that she had soiled herself as she slept. When she brought her fingers to her face, she could smell the blood on them. Am I dying? Then she saw the pale crescent moon, floating high above the grass, and it came to her that this was no more than her moon blood.
_{ADWD - Daenerys X}

And

She rubbed her fingers through the dirt, and grabbed a handful of grass to wipe between her legs. The dragon does not weep. She was bleeding, but it was only woman's blood. The moon is still a crescent, though. How can that be? She tried to remember the last time she had bled. The last full moon? The one before? The one before that? No, it cannot have been so long as that. "I am the blood of the dragon," she told the grass, aloud.
_{ADWD - Daenerys X}

She didn't bear a living child, she apparently miscarried. But that shows her womb can quicken.