Speech Emotion Recognition models typically use single categorical labels, overlooking the inherent ambiguity of human emotions. Ambiguous Emotion Recognition addresses this by representing emotions as probability distributions, but progress is limited by unreliable ground-truth distributions inferred from sparse human annotations. This paper explores whether Large Audio-Language Models (ALMs) can mitigate the annotation bottleneck by generating high-quality synthetic annotations. We introduce a framework leveraging ALMs to create Synthetic Perceptual Proxies, augmenting human annotations to improve ground-truth distribution reliability. We validate these proxies through statistical analysis of their alignment with human distributions and evaluate their impact by fine-tuning ALMs with the augmented emotion distributions. Furthermore, to address class imbalance and enable unbiased evaluation, we propose DiME-Aug, a Distribution-aware Multimodal Emotion Augmentation strategy. Experiments on IEMOCAP and MSP-Podcast show that synthetic annotations enhance emotion distribution, especially in low-ambiguity regions where annotation agreement is high. However, benefits diminish for highly ambiguous emotions with greater human disagreement. This work provides the first evidence that ALMs could address annotation scarcity in ambiguous emotion recognition, but highlights the need for more advanced prompting or generation strategies to handle highly ambiguous cases.