As generative AI is increasingly contributing to the spread of deceptively realistic misinformation, lawmakers have introduced regulations requiring the disclosure of AI-generated content. However, it is unclear if labels reduce the risk of users falling for AI-generated misinformation. To address this research gap, we study the effect of labels on users' perception and the implications of mislabeling, focusing on AI-generated images. We first explored users' opinions and expectations of labels using five focus groups. Although participants were wary of practical implementations, they considered labeling helpful in identifying AI-generated images and avoiding deception. Second, we conducted a survey with 1354 participants to assess how labels affect users' ability to recognize misinformation. While labels reduced participants' belief in false claims supported by AI-generated images, we found evidence of overreliance, leading to unintended side effects: Participants were more susceptible to false claims accompanied by human-made images, and were more hesitant to believe true claims illustrated with labeled AI-generated images.