Most CAV applications, especially those designed for environmental benefits, rely on the assumption that perfect positioning is continuously available. However, this is not the case in real-life situations, for example, when GNSS is used for positioning in urban canyons. Furthermore, very little research has been conducted to evaluate the impacts of positioning accuracy on CAV applications at the traffic level. The objective of our paper is therefore to examine the effect of varying levels of positioning error on an example environmentally-friendly CAV application, Eco Approach and Departure at Signalized Intersections (EAD). Our findings indicate that the energy consumption and travel time of vehicles traversing a road network can be negatively impacted by inaccurate position estimation of the EAD-equipped vehicles. In particular, when the maximum position error exceeds 20 m, the travel time penalty may begin to outweigh the energy savings of the application, especially when congestion is present and all vehicles are equipped with the application.