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This work discusses feasibility aspects of motion planning for groups of agents connected by a range-constrained wireless network. Specifically, we address the difficulties encountered when trajectories are required to preserve the connectedness of the network. The analysis utilizes a quantity called the connectivity robustness of the network, which can be calculated in a distributed fashion, and thus is applicable to distributed motion planning problems arising in control of vehicle networks. Further, these results show that network constraints posed as connectivity robustness constraints have minimal impact on reachability, provided that an appropriate topology control algorithm is implemented. This contrasts with more naive approaches to connectivity maintenance, which can significantly reduce the reachable set.