Air-sea exchange of carbon dioxide (CO$_2$) in the Southern Ocean plays an important role in the global carbon budget. Previous studies have suggested that flow around topographic features of the Southern Ocean enhances the upward supply of carbon from the deep to the surface, influencing air-sea CO$_2$ exchange. Here, we investigate the role of seafloor topography on the transport of carbon and associated air-sea CO$_2$ flux in an idealized channel model. We find elevated CO$_2$ outgassing downstream of a seafloor ridge, driven by anomalous advection of dissolved inorganic carbon. Argo-like Lagrangian particles in our channel model sample heterogeneously in the vicinity of the seafloor ridge, which could impact float-based estimates of CO$_2$ flux.