[Tusjecht]

Spoiler for Asuna & Alicization:

Yes, she does. In fact, she does this twice; the first time, she stalks him all the way to the Ocean Turtle, as the LNs have covered, and the second time...it hasn't been covered yet, but the circumstances of that in the WEB novel was that Asuna was lying right on top of Kirito and she forced persuaded him to Dive in with her.

Edit: Oh, and I take back what I stated a few posts back: there are two more instances when Kirito dual wields. One of the two is covered in Versus, the Accel World crossover side story, the second comes at the ending to Alicization.