If I remember correctly Inari never fed on Harry at all, not even a nibble. The reason being Harry understood right away what was happening and he also had no interest of that kind in a young teenage girl nor fatal statutory rape.
If her Hunger Demon died, she is just a vanilla human, no powers.
Inari stopped with Harry because her lips were burned.
Her eyes flashed pure and empty white, and her skin began to grow luminous and pearlescent. I tried to fumble some words out of my mouth, to tell her to stop. They didn't get past my tingling lips. ... Cold started spreading through me -- delicious, sweet cold that stole warmth and strength even as the pleasure began.
And then the damnedest thing happened.
Inari let out a panicked shriek and staggered back from me. [pp. 154-155 of Blood Rites
That reads like Inari's Hunger was awakened and it was beginning the feeding when the burn shocked Inari out of it.
Piecing the bits from Blood Rites and Bigfoot on Campus together I took it that the lack of knowledge of the Hunger means its first feeding is uncontrolled by the host (you can't control that which you don't know you have to control) and that first killing feed gives the demon a hold on the host it wouldn't otherwise have.
Because of Irwin, Connie has her Hunger awake and intact, but her soul isn't bound by it like those who killed their first lover. She remains an innocent in that way. Not sure what all the ramifications of that might be. She probably still doesn't know to exert control, or how to control the extent of the feeding. With Irwin she doesn't need to worry about it.