User-centric ultra-dense network is envisioned to enable ultra-reliable and low-latency vehicle-to-infrastructure (V2I) communication, by leveraging the diversity gain resulted from the cooperation among multiple roadside units (RSUs) of a virtual cell. In uplink transmission, the same set of co-channel vehicles introduces spatial correlation into the interference powers at cooperative RSUs, which, however, has been ignored for analysis simplification in existing works. In this paper, we develop an analytical framework using stochastic geometry, which resolves the effect of such spatial interference correlation, to evaluate the outage probability and average spatial throughput. Besides the exact analytical results for a double-association case, upper and lower bounds of the outage probability are derived by full-correlation and no-correlation assumptions, respectively. The simulation results show that the effects of the spatial interference correlation are significant under specific conditions, and ignoring the correlation will cause suboptimal network deployment.