Ambient awareness refers to the ability of social media users to obtain knowledge about who knows what (i.e., users' expertise) in their network, by simply being exposed to other users' content (e.g, tweets on Twitter). Previous work, based on user surveys, reveals that individuals self-report ambient awareness only for parts of their networks. However, it is unclear whether it is their limited cognitive capacity or the limited exposure to diagnostic tweets (i.e., online content) that prevents people from developing ambient awareness for their complete network. In this work, we focus on in-wall ambient awareness (IWAA) in Twitter and conduct a two-step data-driven analysis, that allows us to explore to which extent IWAA is likely, or even possible. First, we rely on reactions (e.g., likes), as strong evidence of users being aware of experts in Twitter. Unfortunately, such strong evidence can be only measured for active users, which represent the minority in the network. Thus to study the boundaries of IWAA to a larger extent, in the second part of our analysis, we instead focus on the passive exposure to content generated by other users -- which we refer to as in-wall visibility. This analysis shows that (in line with \citet{levordashka2016ambient}) only for a subset of users IWAA is plausible, while for the majority it is unlikely, if even possible, to develop IWAA. We hope that our methodology paves the way for the emergence of data-driven approaches for the study of ambient awareness.