This paper investigates the relationship between Persuasion Techniques (PTs) and Discourse Relations (DRs) by leveraging Large Language Models (LLMs) and prompt engineering. Since no dataset annotated with both PTs and DRs exists, we took the SemEval 2023 Task 3 dataset labelled with 19 PTs as a starting point and developed LLM-based classifiers to label each instance of the dataset with one of the 22 PDTB 3.0 level-2 DRs. In total, four LLMs were evaluated using 10 different prompts, resulting in 40 unique DR classifiers. Ensemble models using different majority-pooling strategies were used to create 5 silver datasets of instances labelled with both persuasion techniques and level-2 PDTB senses. The silver dataset sizes vary from 1,281 instances to 204 instances, depending on the majority pooling technique used. Statistical analysis of these silver datasets shows that six discourse relations (namely Cause, Purpose, Contrast, Cause+Belief, Concession, and Condition) play a crucial role in persuasive texts, especially in the use of Loaded Language, Exaggeration/Minimisation, Repetition and to cast Doubt. This insight can contribute to detecting online propaganda and misinformation, as well as to our general understanding of effective communication.