Recent technological advancements are making the use of compact, low-cost, low-power mm-wave radars viable for providing environmental awareness in a number of applications, ranging from automotive to indoor mapping and radio resource optimisation. These emerging use-cases pave the road towards networks in which a large number of radar and broadband communications devices coexist, sharing a common spectrum band in a possibly uncoordinated fashion. Although a clear understanding of how mutual interference influences radar and communications performance is key to proper system design, the core tradeoffs that arise in such scenarios are still largely unexplored. In this paper, we provide results that help bridge this gap, obtained by means of an analytical model and extensive simulations. To capture the fundamental interactions between the two systems, we study mm-wave networks where pulsed radars coexist with communications devices that access the channel following an ALOHA policy. We investigate the effect of key parameters on the performance of the coexisting systems, including the network density, fraction of radar and communication nodes in the network, antenna directivity, and packet length. We quantify the effect of mutual interference in the coexistence scenario on radar detection and communication network throughput, highlighting some non-trivial interplays and deriving useful design tradeoffs.