Spectrum pooling is not typically used in current cellular networks, because it only provides a slight performance improvement while requiring heavy coordination among different cellular operators. However, these problems can be potentially overcome in millimeter-wave (mmWave) networks, thanks to the use of beamforming both at base stations and at user equipments. In this paper, we develop a joint beamforming and cell association optimization problem to characterize the performance gain that can be obtained when spectrum pooling is used, as a function of the underlying beamforming and coordination strategies. Our performance analysis reveals that beamforming can substantially reduce the need for coordination and simplify the implementation of spectrum pooling. These benefits are more prominent at higher mmWave frequencies (for example, 73 GHz) due to the possibility of having antenna arrays with more elements within the radome. The results of this paper provides useful insights on the feasibility of spectrum pooling at mmWave networks.