The multi-robot coverage problem is an essential building block for systems that perform tasks like inspection, exploration, or search and rescue. We discretize the coverage problem to induce a spatial graph of locations and represent robots as nodes in the graph. Then, we train a Graph Neural Network controller that leverages the spatial equivariance of the task to imitate an expert open-loop routing solution. This approach generalizes well to much larger maps and larger teams that are intractable for the expert. In particular, the model generalizes effectively to a simulation of ten quadrotors and dozens of buildings in an urban setting. We also demonstrate the GNN controller can surpass planning-based approaches in an exploration task.