Possible, with Nic grabbing it without anyone noticing and taking it with him. However I don't see Nic returning to Hades for it. It may also be possible that Hades has it in his possession, in that case
in my opinion no one else is going to get it.
Agreed, Nic won't return to Hades' vault.
But recall how he hid and retreated at the end of the fight with Michael & Harry? Emphasis on "hid," for our purposes: he vanished from BOTH their views, mid-combat.
I think that demonstrates that Anduriel could cloak Nic during... say... the Dresden vs. Denarian-Gen duel. The big guy was flinging so much rock, collapsing columns, etc... Harry would likely not have noticed a careful and subtle effort by the Master of Shadows.
That's Lasciel, in the bag! Besides... If that WASN'T what he was doing... He was doing something even worse (because Nicodemus).
Then he lurks after the chase, sees Roadkill Gen, and gives the Good Guys a moment to get clear; then moves in to score Ursiel for the twofer.
And we saw how fast he could move, in his dash through the Gate & to the vault-door (where he paused to taunt Harry (& Michael)).
I honestly don't even consider this a WAG, just a most-likely course of events.