I was pointed yesterday to a paper by Pablo Jensen and colleagues on the relationship between outreach activity and academic productivity
Scientists who engage with society perform better academically
Most scientific institutions acknowledge the importance of opening the so-called 'ivory tower' of academic research through popularization, industrial collaboration or teaching. However, little is known about the actual openness of scientific institutions and how their proclaimed priorities translate into concrete measures. This paper gives an idea of some actual practices by studying three key points: the proportion of researchers who are active in wider dissemination, the academic productivity of these scientists, and the institutional recognition of their wider dissemination activities in terms of their careers. We analyze extensive data about the academic production, career recognition and teaching or public/industrial outreach of several thousand of scientists, from many disciplines, from France's Centre National de la Recherche Scientifique. We find that, contrary to what is often suggested, scientists active in wider dissemination are also more active academically. However, their dissemination activities have almost no impact (positive or negative) on their careers.
I think this is a little old now (from 2008) and it would be useful to track down subsequent treatments. Also, the CNRS is probably not the best model for scientists in other systems. An important confounding variable is the amount of teaching that scientists do, which may increase outreach in some ways (by requiring regular practice communicating with students) but takes time away from some opportunities for public engagement.