I would point out the Molly Summoning passage in PT, Jim sets up exactly that scenario in Molly trying to leave a circle the mortal part of her could, but because she is so riddled through with the Mantle, what passed through the circle would not be Molly as she was.
I think this scene was included as a companion to that of the testing of the swords new capabilities, the sword might successfully kill the Hunger BUT the mortal left is not recognisably Thomas.
I think perhaps the way forward is to change the nature of the Hunger, not to kill it, we do not know enough of the White Courts origins whether that is possible. Get the hunger to feed on love rather than life. The Sword of Faith is not the only weapon in Harry’s Arsenal. It is interesting if you look at the Wikipedia article on Cupid (aka Eros or AMOR) the classical depiction does match Thomas’s appearance as we see him in Grave Peril for the first time, and Christian depictions of Cupid as a demon of fornication match the White Court to a T.
If Whamps are the corrupted scion of Cupid, the one thing which might be able to undo the corruption is the grail, a purifier, which means Harry would have to actively seek out Nicky to cure Thomas. That would be fun, and where the sword of faith may come into play in a cure.
If you can cure Thomas, or convert him, it is a potential end of the White Court Vampires, and introduce Thomas to the concept of Monogamy, which he probably thinks is some kind of wood.