@Lily yes she would. The fact that he saved her life and she could be grateful for that aside, at the moment she became the target of nobles. A$$hole as he is, he is her only safety net. If he dies she remains alone without any backing with a target on her back. And even if she miraculously escapes from the people who'd go after her, she'd have to return to her life in slums which is the reason why she started this whole mess in the first place. So yes, obviously she'd be worried about his life no matter how annoying he is.