Available corpora for Argument Mining differ along several axes, and one of the key differences is the presence (or absence) of discourse markers to signal argumentative content. Exploring effective ways to use discourse markers has received wide attention in various discourse parsing tasks, from which it is well-known that discourse markers are strong indicators of discourse relations. To improve the robustness of Argument Mining systems across different genres, we propose to automatically augment a given text with discourse markers such that all relations are explicitly signaled. Our analysis unveils that popular language models taken out-of-the-box fail on this task; however, when fine-tuned on a new heterogeneous dataset that we construct (including synthetic and real examples), they perform considerably better. We demonstrate the impact of our approach on an Argument Mining downstream task, evaluated on different corpora, showing that language models can be trained to automatically fill in discourse markers across different corpora, improving the performance of a downstream model in some, but not all, cases. Our proposed approach can further be employed as an assistant tool for better discourse understanding.