Problems with networks of coupled oscillators arise in multiple contexts, commonly leading to the question about the dependence of network dynamics on network structure. Previous work has addressed this question in Drosophila oogenesis, in which stable cytoplasmic bridges connect the future oocyte to the supporting nurse cells that supply the oocyte with molecules and organelles needed for its development. To increase their biosynthetic capacity, nurse cells enter the endoreplication program, a special form of the cell cycle formed by the iterated repetition of growth and synthesis phases without mitosis. Recent studies have revealed that the oocyte orchestrates nurse cell endoreplication cycles, based on retrograde (oocyte to nurse cells) transport of a cell cycle inhibitor produced by the nurse cells and localized to the oocyte. Furthermore, the joint dynamics of endocycles has been proposed to depend on the intercellular connectivity within the oocyte-nurse cell cluster. We use a computational model to argue that this connectivity guides, but does not uniquely determine the collective dynamics and identify several oscillatory regimes, depending on the timescale of intercellular transport. Our results provide insights into collective dynamics of coupled cell cycles and motivate future quantitative studies of intercellular communication in the germline cell clusters.