That's what compels are for. But given the habits of both Red and White court vampires in the fiction, it's clearly entirely possible for them to feed, and be well-fed, without killing. And if feeding without killing is an option during play, then it should have an effect during play.
In regard to the 'stress as a narrative hit' thing...honestly, it doesn't matter. The power says, "If you cause your target to bleed." So make that a prerequisite: If you want to feed, the target has to be bleeding. Whether he's bleeding from a consequence or from a stress hit doesn't matter. What matters is whether he's bleeding, and yes, it's possible to be bleeding from a stress hit.
Then, in the next exchange after bleeding is established, the character can choose to do a feeding attack, justified in their trying to eat from the previously-established wound.