We explore the use of discourse parsers for extracting a particular discourse structure in a real-world social media scenario. Specifically, we focus on enhancing parser performance through the integration of synthetic data generated by large language models (LLMs). We conduct experiments using a newly developed dataset of 1,170 local RST discourse structures, including 900 synthetic and 270 gold examples, covering three social media platforms: online news comments sections, a discussion forum (Reddit), and a social media messaging platform (Twitter). Our primary goal is to assess the impact of LLM-generated synthetic training data on parser performance in a raw text setting without pre-identified discourse units. While both top-down and bottom-up RST architectures greatly benefit from synthetic data, challenges remain in classifying evaluative discourse structures.