The Conan stories are set in the Hyborian Age, which as I understand is supposed to be a semi-mythical past which existed prior to the "dawn of civilization", and the evidence of which was wiped out, surviving only in myth. It incorporates some "real" stuff, like Atlantean fables, and there are references to Arthuria too, as I recall, not to mention the Aryans.

Pretty much! The Hyborian Age was introduced in the opening to Robert E. Howard's "The Phoenix on the Sword" (Weird Tales Dec 1932):

"KNOW, oh prince, that between the years when the oceans drank Atlantis and the gleaming cities, and the years of the rise of the Sons of Aryas, there was an Age undreamed of, when shining kingdoms lay spread across the world like blue mantles beneath the stars—Nemedia, Ophir, Brythunia, Hyperborea, Zamora with its dark-haired women and towers of spider-haunted mystery, Zingara with its chivalry, Koth that bordered on the pastoral lands of Shem, Stygia with its shadow-guarded tombs, Hyrkania whose riders wore steel and silk and gold. But the proudest kingdom of the world was Aquilonia, reigning supreme in the dreaming west. Hither came Conan, the Cimmerian, black-haired, sullen- eyed,sword in hand, a thief, a reaver, a slayer, with gigantic melancholies and gigantic mirth, to tread the jeweled thrones of the Earth under his sandalled feet." —The Nemedian Chronicles

A few stories later, Howard would sit down and sketch out this setting (including maps), with a long essay titled The Hyborian Age, which was published after his death, first semi-serialized in a fanzine titled The Phantagraph, and then in full as a separate publication from the Los Angeles Science Fiction Society.

This is fairly reflective of the common pseudo-historical thinking that is quite popular even today from known cranks like Graham Hancock.

Not quite. Howard was wearing many of his influences on his sleeve - his correspondence with H. P. Lovecraft in particular goes into some detail about his knowledge of and beliefs regarding history, anthropology, and racialist scientific theories regarding the Irish or Celts (influenced in part by the Book of Invasions), and he touched on occult-esque theories such as the Theosophical accounts of Atlantis and Lemuria.

Yet the Hyborian Age as Howard developed it was, like J. R. R. Tolkien's later Middle Earth legendry, not created out of whole cloth by developed a bit at a time, expressed in many stories that predate the first Conan story set in the Hyborian Age. So for example, "The Hyborian Age" essay references the Thurian Age, which was the setting for his earlier stories of Kull of Atlantis (the first Conan story, "The Phoenix on the Sword" was actually a re-write of a Kull story, "By This Axe I Rule"). Elements of Atlantean religion and culture (as Howard conceived them), appeared in stories as disparate as the Solomon Kane story "The Moon of Skulls" (Weird Tales Jun-Jul 1930) and "The Gods of Bal-Sagoth" (Weird Tales Oct 1931). Kull had a crossover with another of Howard's creations, the Pictish king Bran Mak Morn, in "Kings of the Night" (Weird Tales Oct 1930)...and I could go on.

Howard never pretended that his pseudo-history was in any way "real" - he added the disclaimer to his essay:

Nothing in this article is to be considered as an attempt to advance any theory in opposition to accepted history. It is simply a fictional background for a series of fiction-stories. When I began writing the Conan stories a few years ago, I prepared this 'history' of his age and the peoples of that age, in order to lend him and his sagas a greater aspect of realness. And I found that by adhering to the 'facts' and spirit of that history, in writing the stories, it was easier to visualize (and therefore to present) him as a real flesh-and-blood character rather than a ready-made product. In writing about him and his adventures in the various kingdoms of his Age, I have never violated the 'facts' or spirit of the 'history' here set down, but have followed the lines of that history as closely as the writer of actual historical-fiction follows the lines of actual history. I have used this 'history' as a guide in all the stories in this series that I have written.

Now, in his letters Howard does occasionally present his own theories with regard to history, but while those informed his particular style and conception, he was always careful to draw a distinction between what really happened and what he wrote as fiction. (Outside of a few tall tales in his letters, but those are more in the way of dramatic license.)

To what extent was Howard just looking to make up a fun setting for his stories, and to what extent does this reflect actual thinking and understanding that we would label today as pseudohistory/archaeology/anthropology etc?

Mostly, Howard was doing something a little rare even for the pulps of the day: worldbuilding. He wasn't as desirous as H. P. Lovecraft to craft a Mythos for different writers to use, but many of his stories have tie-ins, connections, and elements that make them part of a bigger and more fully realized setting than other pulp fantasies at the time. This was part of an effort to increase the verisimilitude of the stories, and it gave them added scope and punch.

If Howard had published this as non-fiction, that would be something we would label as pseudo-history. The Texas pulpster never wrote with the intention of deceiving the audience, and "The Hyborian Age" essay is not comparable to books like William Scott-Elliott's The Story of Atlantis and the Lost Lemuria (1925), despite a few gross similarities in content.

Indeed, one of the aspects of Howard's writing that exasperated his fellow pulpsters was the tendency to borrow wholesale from different historical periods in creating his Hyborian Age. One such letter:

The only flaw in this stuff is REH’s incurable tendency to devise names too closely resembling actual names of ancient history—names which, for us, have a very different set of associations. In many cases he does this designedly—on the theory that the familiar names descend from the fabulous realms he describes—but such a design is invalidated by the fact that we clearly know the etymology of many of the historic terms, hence cannot accept the pedigree he suggests. Price & I have both argued with Two-Gun on this point, but we make no headway whatsoever. The only thing to do is to accept the nomenclature as he gives it, wink at the weak spots, & be damned thankful that we can get such vivid artificial legendry. Howard is without question the most vigorous & spontaneous writer now contributing to the pulps—the nearest approach (although he wouldn’t admit it himself) to a sincere artist. He puts himself into his work as none of the regulation hacks do.

—H. P. Lovecraft to Donald A. Wollheim, 7 Oct 1935, Letters to Robert Bloch and Others 319