I highly doubt that it matters if it's a Hawke that he knows or not. He will likely bond with her as instantly as he did in Kirkwall the first time with the Hawke any of us knew.

[Because, as far as he can tell, Hawke will be Hawke, no matter gender or world.

Not that that matters now that he has Iona in his arms. It's as perfect as the other times they've been in this same position. Perhaps more so because he feels less inclined to let her go, less guilty that he might be forcing her into something she might not want.

When she wraps her arms around his neck, he smiles into her lips.]

You are incorrigible, my lady. And extremely irresistible.