At millimeter wave (mmWave) frequencies, signals are prone to blocking by objects in the environment, which causes paths to go from line-of-sight (LOS) to non-LOS (NLOS). We consider macrodiversity as a strategy to improve the performance of mmWave cellular systems, where the user attempts to connect with two or more base stations. An accurate analysis of macrodiversity must account for the possibility of correlated blocking, which occurs when a single blockage simultaneously blocks the paths to two base stations. In this paper, we analyze the macrodiverity gain in the presence of correlated random blocking and interference. To do so, we develop a framework to determine distributions for the LOS probability, SNR, and SINR by taking into account correlated blocking. We consider a cellular uplink with both diversity combining and selection combining schemes. We also study the impact of blockage size and blockage density. We show that blocking can be both a blessing and a curse. On the one hand, the signal from the source transmitter could be blocked, and on the other hand, interfering signals tend to also be blocked, which leads to a completely different effect on macrodiversity gains. We also show that the assumption of independent blocking can lead to an incorrect evaluation of macrodiversity gain, as the correlation tends to decrease macrodiversity gain.