She'd probably starve after a long enough period of time. She mentions drinking from blood bags, which there wouldn't be much reason to do if she didn't need blood (as it'd be simpler esp in the human world where she went to school to simply live on human food). It's possible that exerting her vampire powers less would lessen the need for blood but I don't think this was ever implied in the manga. As to what happens when she starves... I'd say rather than death probably a state of torpor from which she cannot wake until blood is introduced into her system (guess based largely on the fact that Alucard was able to be "dead" for so long in a torpor like state).
Eh Alucard isn't her father, Issa is and Alucard was sealed by Moka mom's he had blood he was just magically sealed, it's unknown what happen's when a vampire doesn't drink in this series but based on what I've read death seems to be the answer, they never really stated it but in most cases when a vamp doesn't feed death is always the outcome since we have no cannon answer, the death answer is the only reasonable one to assume.