No, his responses would be deleted as personal anecdotes for citing Herodotus.
But Herodotus does cite his sources a bunch...
e.g. from The Histories
Book I: "These are the researches of Herodotus of Halicarnassus, which he publishes, in the hope of thereby preserving from decay the remembrance of what men have done, and of preventing the great and wonderful actions of the Greeks and the Barbarians from losing their due meed of glory; and withal to put on record what were their grounds of feuds. According to the Persians best informed in history, the Phoenicians began to quarrel...Thus much I know from information given me by the Delphians; the remainder of the story the Milesians add."
Book II: "That these were the real facts I learnt at Memphis from the priests of Vulcan. That these were the real facts I learnt at Memphis from the priests of Vulcan. The Greeks, among other foolish tales, relate that Psammetichus had the children brought up by women whose tongues he had previously cut out; but the priests said their bringing up was such as I have stated above. I got much other information also from conversation with these priests while I was at Memphis, and I even went to Heliopolis and to Thebes, expressly to try whether the priests of those places would agree in their accounts with the priests at Memphis. The Heliopolitans have the reputation of being the best skilled in history of all the Egyptians. What they told me concerning their religion it is not my intention to repeat, except the names of their deities, which I believe all men know equally. If I relate anything else concerning these matters, it will only be when compelled to do so by the course of my narrative."
Book III: "The Egyptians, however, claim Cambyses as belonging to them, declaring that he was the son of this Nitetis. It was Cyrus, they say, and not Cambyses, who sent to Amasis for his daughter. But here they mis-state the truth. Acquainted as they are beyond all other men with the laws and customs of the Persians, they cannot but be well aware, first, that it is not the Persian wont to allow a bastard to reign when there is a legitimate heir; and next, that Cambyses was the son of Cassandane, the daughter of Pharnaspes, an Achaemenian, and not of this Egyptian. But the fact is that they pervert history in order to claim relationship with the house of Cyrus. Such is the truth of this matter.
I have also heard another account, which I do not at all believe: that a Persian lady came to visit the wives of Cyrus, and seeing how tall and beautiful were the children of Cassandane, then standing by, broke out into loud praise of them, and admired them exceedingly. But Cassandane, wife of Cyrus, answered, "Though such the children I have borne him, yet Cyrus slights me and gives all his regard to the new-comer from Egypt." Thus did she express her vexation on account of Nitetis: whereupon Cambyses, the eldest of her boys, exclaimed, "Mother, when I am a man, I will turn Egypt upside down for you." He was but ten years old, as the tale runs, when he said this, and astonished all the women, yet he never forgot it afterwards; and on this account, they say, when he came to be a man, and mounted the throne, he made his expedition against Egypt."
Book IV: "According to the account which the Scythians themselves give, they are the youngest of all nations. Their tradition is as follows. A certain Targitaus was the first man who ever lived in their country, which before his time was a desert without inhabitants. He was a child- I do not believe the tale, but it is told nevertheless- of Jove and a daughter of the Borysthenes."
Book V: "According to the account which the Thracians give, the country beyond the Ister is possessed by bees, on account of which it is impossible to penetrate farther. But in this they seem to me to say what has no likelihood; for it is certain that those creatures are very impatient of cold. I rather believe that it is on account of the cold that the regions which lie under the Bear are without inhabitants. Such then are the accounts given of this country, the sea-coast whereof Megabazus was now employed in subjecting to the Persians."
Book VI:"Thus much is related by the Lacedaemonians, but not by any of the other Greeks; in what follows I give the tradition of the Greeks generally. The kings of the Dorians (they say)- counting up to Perseus, son of Danae, and so omitting the god- are rightly given in the common Greek lists, and rightly considered to have been Greeks themselves; for even at this early time they ranked among that people. I say "up to Perseus," and not further, because Perseus has no mortal father by whose name he is called, as Hercules has in Amphitryon; whereby it appears that I have reason on my side, and am right in saying, "up to Perseus." If we follow the line of Danad, daughter of Acrisius, and trace her progenitors, we shall find that the chiefs of the Dorians are really genuine Egyptians. In the genealogies here given I have followed the common Greek accounts.
According to the Persian story, Perseus was an Assyrian who became a Greek; his ancestors, therefore, according to them, were not Greeks. They do not admit that the forefathers of Acrisius were in any way related to Perseus, but say they were Egyptians, as the Greeks likewise testify."
...and so on and so forth. They're not footnotes, but he's certainly telling his audience where his stuff came form.
He did cite sources. But "the Phoenicians told me" probably wouldn't be considered a credible source under the rules.
He'd also get in trouble for speculation. Ask Herodotus why the Nile floods every year sometime!
One thing he does right is he often does try to provide several plausible theories from various (usually unverifiable) sources. He doesn't usually assert his own speculation as truth. Or put forth one theory and ignore others. In addition to his own speculation, Herodotus will also tell you that some think the Nile floods because of melting snows. Which is crazy because everyone knows it gets hotter the further south you go! So why would there be snow? (He doesn't know about the equator.) But he does present this theory as well as his own rather than assert his own version as the truth. And, of course, this alternate theory he provides us is the true one. The more famous example is that he tells us the Phoenicians claim they circumnavigated Africa. And they say the sun was on the other side when they did so. Herodotus is generally skeptical of Phoenicians and he thinks that's just nuts (why would the sun change position in that way?) But, of course, that is what happens. It doesn't prove they did so but it is some of the only semi-credible evidence to think they may have. And we wouldn't have that if Herodotus didn't quote his sources somewhat faithfully regardless of his own skepticism.
Providing several credible interpretations on incidents that lack complete factual veracity regardless of the author's personal beliefs or opinions is usually thought of well. And it's why I think Herodotus is a better historian than he is given credit for. Even though we'll never be able to track down his sources.
Drat
He would fare better than Thucydides' breathless fanfic. Herodotus at least recognizes the idea that sources exist and history is interpretation.
Don't forget that the rules only state you have to cite sources when requested. Maybe nobody ever asked him?
His use of anecdotal or oral history is more problematic. But if you're writing the first history book, what else are you going to do? I'm sure he'd have a lot to say about the topic of Oral History that was the theme the other week.
I wonder if maybe he did cite sources and had it all written down but those pages didn't survive. I cannot find exactly if Histories was found at one single site or if there were many copies of varying pages intact.
I wrote up a long response about the historian's fallacy, but I couldn't really make it work well.
From my experience as a programmer, self-taught programmers have a much different style and different conceits than programmers who learned from others, and went to school for it. I take shortcuts, I'm reckless in ways that a good teacher weeds out with considered recommendations of years of personal and collected experience. And I had the internet-- I've read about a programmer in the Outback of Australia as a kid who wrote his own operating system by copying DOS functionality.
The implicit tradeoff, I think, is that those who learn without outside correction have to develop their own value systems and guidelines, think about what matters and what might work for future needs, while 'taught' students have most often learned by being told, so they might continue expecting direction, even if that direction represents models with misguided predictions.
Herodotus was flying blind, and yet he flew so well that people still define their choices by his successes and failures. /r/AskHistorians has a rich set of maps that show the pitfalls of mistakes and fallacies that we don't necessarily have to fall into, because Herodotus did.