Not really. There is a distinct and substantial difference between the lance of longinus, Mjolnir, the unnamed sword Beowulf found in Grendel's mother's cave, the two magic swords in the saga of Kornack the skald, and David's sling and Samson's jawbone.
First, the lance of Longinus was thought to have specific powers inherent in it. It made its owner invincible, if used to strike someone, it might bring a curse upon the kingdom, etc. These powers were not merely demonstrations that if God is on your side the weapon doesn't matter. Rather, they are side effects of the object's sacredness and the blasphemy that would be striking someone with it. The sword Beowulf found in Grendel's mother's cave was forged by giants and while Hrunting was unable to kill Grendel's mother, the sword was able to injure her. In the epic, God's favor was neither here nor there since it is a self-consciously Christian retelling of a story about earlier pagans who did not know God. The same is true of the magic swords in the story of Kornack. They had special powers that did not connote divine favor and at least the one that Kornack borrowed had to be prepared with a special ritual in order to function.
The same is true in Greek myth. When Perseus went to fight Medusa, he was given the Aegis to use, but the Aegis was not a sign of divine favor; instead the Aegis was the manifestation of divine favor. The gods favored Perseus therefore they gave him a divine shield (and a bunch of other magic stuff).
In norse myth, Thor's hammer is special, independent of Thor. Thor is special, partly because he has the strength to wield Mjolnir. But if Mjolnir is stolen, Thor can't pick up any old hammer and have it do the same thing. The powers are inherent in Mjolnir not in Thor.
The stories of David and Samson are the exact opposite. There was nothing special about David's sling. It wasn't long before Jonathan gave him a bow and he used that. When he was on the run from King Saul, he used Goliath's sword for a while. As far as the story reads, he never used a sling again after that battle, it was just what he happened to have at the time. The point of the story is not that God favored David and therefore God gave him a magic sling or gave him a weapon that was otherwise powerful. The point is that God favored David and therefore David won despite his inadequate weaponry. In D&D terms, that's more analogous to a pre-erratta Divine Favor spell rather than a magic weapon. The same is true of Samson and the jawbone of an ass. He wasn't carrying the jawbone and when he finished killing the thousands of Philistines, he didn't keep it. It was simply the only tool he had handy at a time. The story of Samson is very clear that the divine favor that was upon Samson was his strength (and possibly some form of increased skill or invulnerability since strength alone wouldn't stop a spear, arrow or sling bullet from hitting him and something obviously did). The jawbone of an ass is simply the nearest tool at hand; it was used when necessary and discarded when unneeded. That seems more like (pre errata) Righteous Might and maybe an intensified bull's strength than a magic weapon to me.
Really, unless a story claims that a weapon has some special quality, it doesn't seem appropriate to call it a magic weapon in these terms. There's as much reason to call Seargent Rock's gun magic as there is to call David's sling, Samuel's jawbone of an ass, Johnathan's spear, Ehud's dagger, etc. magic. If you want a biblical magic weapon, you're better off looking at the Cherub with the flaming sword set to guard the garden of eden in Genesis.
