Fragmentation in road networks and hierarchical imbalances among nodes increase circulation impedance in China’s county-level delivery networks, hindering efficient county–township–village circulation. This study integrates spatial syntax, complex network analysis, hierarchical connection-cost analysis, and a coupling–coordination degree model to develop a network evaluation framework for identifying structural bottlenecks and analyzing circulation efficiency. Using eight counties in Shaanxi Province as empirical cases, we quantify road-network accessibility using a spatial syntax axial model and examine hierarchical node organization across county, township, and village tiers using complex network indicators. Network-level circulation efficiency is analyzed using road accessibility, hierarchical connection costs, county–village connection impedance, and average path length. Correlation and regression analyses are further used to examine the relationship between morphology–structure coordination and network impedance. The results show that higher road-network integration is generally associated with lower hierarchical connection costs, and higher morphology–structure coordination is significantly associated with lower county–village connection impedance and shorter average path length. The proposed network-level evaluation framework provides a structural basis for identifying accessibility deficiencies, hierarchical connectivity constraints, and morphology–structure mismatches, thereby informing efforts to reduce circulation impedance in county–township–village delivery networks.