Aeronautical Engineers the aircraft people use for business and holidaying would not be in the sky, it cannot be contested that society depends heavily on travel via aircraft.

 Aeronautical Engineer will provide the solution to increase overall aircraft efficiency, thereby helping to drive down the levels of emissions current aircraft produce. 

Aeronautical Engineers also help put the satellites in to space, the satellites we rely on for weather information, geospatial mapping data, environmental monitoring, telecommunications and research. So in answer to the question I feel aerospace engineering plays a major role in society, producing and developing a lot of the technology we rely on heavily.