Was Olaf One-Eye a fraud?

It's difficult to say. The Dragonborn encounters resistance during the quest to recover King Olaf's Verse for the Bard's College, including a duel with Olaf's re-animated corpse (or at the last, an observation of such a duel between Olaf and Svaknir's ghost).

One could argue that Olaf's desire to prevent anybody from seeing the verse must mean that the verse describes the truth; why else would he want to suppress it?

But it's also possible that Olaf sought to keep the verse buried because it was libelous and threatened to damage his heritage, which is an important cultural touchstone of the Nord race.

Further, it's possible that Olaf himself did not arrange to be re-animated in guardianship of the verse, and that some third-party forcibly re-animated him as a form of (perhaps ironic) revenge.

The game doesn't offer much evidence either way. If you speak to Olaf in Sovngarde under certain conditions, he will say:

You freed Svaknir, a fool of a poet, but an honest enemy who has earned my respect. Sadly, he's now lost in the soul-snaring mist - defeat Alduin, and his doom avert - I hope to greet him in this Hall as a friend.

Unfortunately this doesn't offer much clarification - only that Svaknir and Olaf did not particularly like each other, which could be the attributable to any of the above possibilities. The dialog does suggest, however, that Olaf is (or at least became before death) an honorable warrior, which leads me to address your second point:

If we assume for the sake of argument that Olaf did fabricate (or more specifically, embellished upon) the tale of Numinex's capture, that doesn't necessarily preclude him from reaching Sovngarde after death.

The Road to Sovngarde states that "Nords who prove themselves in battle awaken in the realm after death." Further, from Sovngarde, a Reexamination we can read that "Sovngarde [was] built by the god Shor to honor those Nords who have proven their mettle in war," and later that "in the end, all valiant Nords can enter Sovngarde."

There appears to be no lore suggesting that a single instance of dishonesty disqualifies one for entrance to Sovngarde: you only need to die bravely, in battle. You do not necessarily need to be a good person.

Even if you don't buy that argument, Olaf was known (after the Numinex events) for subjugating the wilds of the Reach and for helping to restore Skyrim after the War of Succession, which can be considered pretty "heroic" deeds.