Will it? She is too independent a thinker to be either.
Jack Murphy half-truthed Harry, which shows that he's still pretty much an independent thinker, while working for the White God / Uriel.
Gard was pretty much acting independently in the Heorot.
I don't think they lose their capacity for independent thinking or even action.
As long as the soul is there, they're still themselves, with their good traits and bads. Look at Harry, he maybe changed in some measure since becoming the Winter Knight, and you can say it's a struggle for the soul, but he's still himself.