We show that the "dark condensates" that arise when excitons form a Bose-Einstein condensate in a material with an indirect bandgap are not completely dark to optical emission. Rather, such states are "leaky condensates" in which optical emission is facilitated by many-body interactions. We analyze the properties of these leaky condensates in the context of twisted bilayers of transition metal dichalcogenides, which host strongly interacting excitons and an indirect bandgap. We show that, even though excitonic condensates in these materials can break translational symmetry, direct emission remains forbidden by a robust rotational symmetry. The optical signatures at low temperatures are dominated by the interaction-driven "leaky" emission, with distinctive qualitative features.