Yes, the Pathfinder FAQ is RAW - inasmuch as RAW is definable.
The Pathfinder FAQ is attached to the relevant product pages, it is written by the game designers, and considered authoritative by the community.
1) The FAQ considers itself official in its text - and it notes explicitly when it is making unofficial pronouncements, e.g.
Technically the item-pricing formula in the Core Rulebook allows for items like that, but officially the game should only have even-numbered enhancement bonuses to ability scores.
Meanwhile, as a house rule (not an official update to the rules), it's fair to allow someone to use the Widen Spell feat on a line spell and actually double its range. You are, after all, increasing the level by +3, and if you're casting lightning bolt as a 6th-level spell, you ought to at least be able to get a 240-foot bolt out of it.
2) The designers consider the FAQ to be official - and that was widely discussed during the entire process of coming up with it; it replaced the previous process of "official declarations" just being made in the messageboards (reference). The Rules FAQ, And How To Use It on the Paizo boards is the official guide to the FAQ itself. It states (emphasis mine):
The FAQ system was built to allow players and GMs to draw attention to unclear, confusing, or incorrect parts of the game rules and get official answers from the designers. It is not intended to create official rulings for every possible corner case or combination of the rules. Paizo firmly believes it is the privilege and responsibility of the GM to make rulings for unusual circumstances or unusual characters.
3) The Pathfinder community considers the FAQ to be official - it is official in Pathfinder Society and other Pathfinder community sources distinguish between the "official FAQ" and other sources. And that's really the most important point - in general real Pathfinder gamers consider it official and therefore people use it for their games. Considering it "not RAW" based on some legalistic argument is your right, but it will go against the expectations of the vast majority of Pathfinder play groups.
4) Furthermore - it's helpful and well reasoned, and is the only channel for any clarifications short of errata worked into the books themselves. Because of page numbering, the amount of change/clarification that can go into a printed book is practically minimal, meaning that this is the most reasonable path for all publishers to use to clarify their rules short of an entirely new edition.
Therefore using the FAQ is a perfectly acceptable way to answer a RAW question. If the asker, or any other voters, don't like a specific FAQ ruling or consider it binding, they may vote their conscience of course. As stated in The Rules FAQ And How To Use It,
I don't like the answer in the FAQ. What can I do?
If you have found rules that appear to override a FAQ, post about it as a reply to the thread and open up the idea for more discussion. What you found might be an exception to the rule, or it might be the evidence to overturn the ruling.
If you disagree with a ruling but don’t have any additional evidence to show that the ruling is incorrect, accept the ruling and move on (restating your points from earlier in the discussion is not “additional evidence”). Remember that you can house rule it for your home campaign.
But it's a fuzzy distinction.
What is "official" or "RAW" really? As a given gaming group, you can allow some but not all books. You can not allow parts of books. You can not allow the FAQ, you can disagree with specific rulings from the FAQ, you can not allow whatever you want. You can say "if it's not printed on paper it doesn't count, I don't care what every single person working at Paizo says or what any other player or GM says." The Paizo staff are very up front about saying it's "your game, your rules" and their interest in having a One True Way From Which You May Not Deviate is minimal.
Trying to adhere to "a RAW interpretation" as if there is a single strict such thing is as logically erroneous as claiming there's "one" fundamentalist literal interpretation of the Bible - that's not how human writing and cognition works. The very question that spawned this was over a rule that pretty much everyone finds to be clear and unambiguous, but there's always one or two people who find the wording to not quite gel with them.
It's the same with the claim that the 3.5e FAQ isn't official. It is useful but imperfect, but some people "don't like it" and therefore exclude it even when it doesn't conflict with the rules. And that's fine.
You can try to make a "RAW but not official" distinction - but why? So you can build CharOpped characters on a board that exploit loopholes in the printed text that have already been clarified in intent by the designers? So that you can "put one over" on someone who hasn't read the FAQ? What exactly is the value of trying to artificially distinguish between "rules the designers wrote here" versus "rules the designers wrote there," except if you don't believe you have discretion over the rules in the first place - which Paizo tells you that you do (see the quote above)? In the end, insistence on some legal-type reading of RAW is not appropriate for Pathfinder by explicit declaration of the Pathfinder role-playing game and its designers.