Most of the existing studies on the freeway hard-shoulder-running (HSR) strategy only focus on the traffic flow with human-driven vehicles (HDVs) but neglect the potential impacts of connected automated vehicles (CAVs) with various penetration rates on the macroscopic traffic flow. The purpose of this paper is to ascertain whether the effects of mixed traffic flow for the freeway HSR strategy differ from those of a traditional traffic flow or not. In this research, a sophisticated methodology is employed, integrating microscopic simulation with factorial experimental design. By meticulously examining and statistically analyzing the simulation results, significant and novel insights are obtained. We find a complex interplay between the penetration rate of CAVs and HSR strategy on traffic flow efficiency and safety metrics. Without HSR, the traffic flow efficiency does not exhibit an immediate enhancement as the penetration rate increases. Instead, a notable improvement in overall traffic flow efficiency is observed only when the penetration rate attains a specific threshold. After implementing the HSR, the penetration rate of CAVs has a pronounced positive influence both on the traffic efficiency and safety, regardless of the prevailing traffic flow conditions. However, different speed limits for the HSR can lead to varying degrees of efficiency improvement under different traffic demands. Within a penetration rate range of 0.4 to 0.7 during the congested traffic flow, the traffic efficiency achieved at a speed limit of 120 km/h does not necessarily exceed that achieved at a speed limit of 80 km/h. Finally, we observe that the opening of hard shoulders would result in a decrease in traffic safety under congested traffic conditions. This finding provides important guidance for determining the appropriate timing of hard shoulder utilization in mixed traffic flow scenarios in the future.