It's possible, but questionable.
It certainly seems natural that opposing the Night King would be something a new Azor Ahai would be into, but it's all guesswork as to whether or not that would be his or her specific, ordained purpose.
She seems to fit the stated criteria of the prophecy poorly:
- Not a male
- Wrong lineage
- Circumstances of birth unknown
- She certainly isn't holding Lightbringer (yet, at least)
Any and all of those can be corrected with more expansive interpretations of the prophecy, but twisting the prophecy to fit events is not the same as events fitting the prophecy.
After the most recent episode, Arya qualifies well enough-- she did a momentous and consequential thing, upon which the fate of all in Westeros (at least!) depended, and that thing seems to be up R'hllor's alley. And, through Melisandre's interactions with Arya, R'hllor was at least tangentially involved in making that happen. Unless a more obvious candidate comes up soon, that would probably be enough for followers of R'hllor to decide that Arya really was Azor Ahai (or the PWWP), and any details from the prophecy that don't fit will be classified as those read wrongly by people.
But one of the recurring themes in GoT is that prophecies aren't worth a whole lot. There are some that pay off, really specifically and very accurately:
Cersei's fortune from Maggie, for instance. The predictions about her and Robert's children (non-overlapping!) seem very accurate, at least on Cersei's side. We can't really evaluate Robert's.
But others wither away to nothing:
The prophecy that Drogo and Daenerys' child would be the Stallion That Mounts the World, leading to an era of Dothraki ascendancy.
Some prophecies are inherently unreliable, and pretty vague in detail:
Mirri Maz Duur makes some claims about Daenerys being betrayed three times, for specific reasons. This leads to lots of guessing about which events might qualify, but Mirri may not wish Daenerys well at all, and may not have been interested in providing her with accurate information. And a powerful noble in Westeros is likely to be betrayed plenty of times, making the claim a safe cold-reading bet.
And that's to say nothing of the fact that prophecies are perceived and interpreted by people, who could very well be wrong about what they mean:
Melisandre and Stannis both read futures in the flames regarding the siege of Winterfell while it's held by the Boltons. Things don't work out as they expected.
So, with those in mind, I'll posit that the existence of a prophecy regarding Azor Ahai is basically irrelevant to events-- prophecies are common and don't have much currency.
Even to the extent that we disregard that, it's not totally clear exactly what Azor Ahai did the first time around (in a broad sense; we know how he made his sword, but to what purpose is less clear), nor is it totally clear what his new incarnation would be intended to do. We also don't know very much about what the Prince Who Was Promised is to do, in the event that this is a different personality from Azor Ahai.
tl;dr: Assuming that a GoT prophecy is accurate gives that prophecy way too much credit. Had Arya not done what she did in the most recent episode, there wouldn't even be a question that she might fit (see the thread linked in the question), despite that event not even being referred to in the Azor Ahai prophecy.
The evidence that Arya is Azor Ahai reborn is weak, weaker for her than several other characters even now, and the idea that someone must be Azor Ahai reborn already takes us beyond evidence anyhow.