The Opportunistic Large Array (OLA) is a simple form of cooperative transmission, in which a group of single-antenna nodes decode the same packet, then a short time later relay the packet simultaneously in orthogonal or space-time coded channels. The authors have previously shown that OLA transmissions can be adequately synchronized so they appear to a receiver as having come from a conventional array with co-located antennas doing transmit diversity. OLAs have been considered as a basis for rapid single-packet broadcasting in multi-hop networks, however, there are few studies that consider OLA broadcasting of multiple co-channel packets. Using the continuum assumption (approximated by high density networks), we focus on broadcast throughput optimization, as determined by the packet insertion rate at the source. We consider spatial pipelining, which means broadcasting a packet before the previous co-channel packet has cleared the network. We show theoretically that for infinitely large networks the feasibility of spatial pipelining depends on the path loss exponent. For finite networks, we study the propagation behavior of spatially pipelined packets using numerical analysis.