Intelligent reflecting surface (IRS) is a new and promising paradigm to substantially improve the spectral and energy efficiency of wireless networks, by constructing favorable communication channels via tuning massive low-cost passive reflecting elements. Despite recent advances in the link-level performance optimization for various IRS-aided wireless systems, it still remains an open problem whether the large-scale deployment of IRSs in wireless networks can be a cost-effective solution to achieve their sustainable capacity growth in the future. To address this problem, we study in this paper a new hybrid wireless network comprising both active base stations (BSs) and passive IRSs, and characterize its achievable spatial throughput in the downlink as well as other pertinent key performance metrics averaged over both channel fading and random locations of the deployed BSs/IRSs therein based on stochastic geometry. Compared to prior works on characterizing the performance of wireless networks with active BSs only, our analysis needs to derive the power distributions of both the signal and interference reflected by distributed IRSs in the network under spatially correlated channels, which exhibit channel hardening effects when the number of IRS elements becomes large. Extensive numerical results are presented to validate our analysis and demonstrate the effectiveness of deploying distributed IRSs in enhancing the hybrid network throughput against the conventional network without IRS, which significantly boosts the signal power but results in only marginally increased interference in the network. Moreover, it is unveiled that there exists an optimal IRS/BS density ratio that maximizes the hybrid network throughput subject to a total deployment cost given their individual costs, while the conventional network without IRS is generally suboptimal in terms of throughput per unit cost.