Deep reinforcement learning (DRL) has been extensively applied to Multi-Unmanned Aerial Vehicle (UAV) network (MUN) to effectively enable real-time adaptation to complex, time-varying environments. Nevertheless, most of the existing works assume a stationary user distribution (UD) or a dynamic one with predicted patterns. Such considerations may make the UD-specific strategies insufficient when a MUN is deployed in unknown environments. To this end, this paper investigates distributed user connectivity maximization problem in a MUN with generalization to arbitrary UDs. Specifically, the problem is first formulated into a time-coupled combinatorial nonlinear non-convex optimization with arbitrary underlying UDs. To make the optimization tractable, a multi-agent CNN-enhanced deep Q learning (MA-CDQL) algorithm is proposed. The algorithm integrates a ResNet-based CNN to the policy network to analyze the input UD in real time and obtain optimal decisions based on the extracted high-level UD features. To improve the learning efficiency and avoid local optimums, a heatmap algorithm is developed to transform the raw UD to a continuous density map. The map will be part of the true input to the policy network. Simulations are conducted to demonstrate the efficacy of UD heatmaps and the proposed algorithm in maximizing user connectivity as compared to K-means methods.