To address the difficulty of efficiently coordinating demand-side resources in distribution networks with high renewable-energy penetration when model information is incomplete, this paper proposes a data-driven dispatch method based on an Input Convex Neural Network (ICNN). Branch-capacity and nodal-voltage security constraints are represented separately by two signed maximum-violation functions, which are learned from operational samples by an ICNN and embedded as convex surrogate constraints in the dispatch problem. Once trained, the online dispatch stage does not explicitly invoke the network topology, line parameters, or power-flow equations. The method is evaluated on the IEEE 33-bus distribution system and compared with an exact-model benchmark solved by an Interior Point Optimizer (IPOPT). The ICNN predictions closely match the power-flow results, and the resulting dispatch decisions are close to the IPOPT benchmark while requiring substantially less solution time. To mitigate false-safety risks caused by neural-network approximation error, safety margins are further constructed from upper quantiles of dangerous one-sided residuals on an independent calibration set. Across 3,600 hourly AC power-flow checks for 150 independent daily scenarios, the 99% quantile-margin scheme exhibits no positive voltage or branch violation; all 150 test days satisfy the network hard constraints defined in this study within the prescribed operating domain.