Debate naturalness ranges on a scale from small, highly structured, and topically focused settings to larger, more spontaneous and less constrained environments. The more unconstrained a debate, the more spontaneous speakers act: they build on contextual knowledge and use anaphora or ellipses to construct their arguments. They also use rhetorical devices such as questions and imperatives to support or attack claims. In this paper, we study how the reconstruction of the actual debate contributions, i.e., utterances which contain pronouns, ellipses and fuzzy language, into full-fledged propositions which are interpretable without context impacts the prediction of argument relations and investigate the effect of incorporating contextual information for the task. We work with highly complex spontaneous debates with more than 10 speakers on a wide variety of topics. We find that in contrast to our initial hypothesis, reconstruction does not improve predictions and context only improves them when used in combination with propositions.