The collective operation of robots, such as unmanned aerial vehicles (UAVs) operating as a team or swarm, is affected by their individual capabilities, which in turn is dependent on their physical design, aka morphology. However, with the exception of a few (albeit ad hoc) evolutionary robotics methods, there has been very little work on understanding the interplay of morphology and collective behavior. There is especially a lack of computational frameworks to concurrently search for the robot morphology and the hyper-parameters of their behavior model that jointly optimize the collective (team) performance. To address this gap, this paper proposes a new co-design framework. Here the exploding computational cost of an otherwise nested morphology/behavior co-design is effectively alleviated through the novel concept of ``talent" metrics; while also allowing significantly better solutions compared to the typically sub-optimal sequential morphology$\to$behavior design approach. This framework comprises four major steps: talent metrics selection, talent Pareto exploration (a multi-objective morphology optimization process), behavior optimization, and morphology finalization. This co-design concept is demonstrated by applying it to design UAVs that operate as a team to localize signal sources, e.g., in victim search and hazard localization. Here, the collective behavior is driven by a recently reported batch Bayesian search algorithm called Bayes-Swarm. Our case studies show that the outcome of co-design provides significantly higher success rates in signal source localization compared to a baseline design, across a variety of signal environments and teams with 6 to 15 UAVs. Moreover, this co-design process provides two orders of magnitude reduction in computing time compared to a projected nested design approach.