Joint chance-constrained optimal power flow (JCC-OPF) is a promising tool for managing distributed renewable generation uncertainties. However, existing works are usually based on power flow equations, which require accurate network parameters that may be unobservable in many distribution systems. To address this issue, this paper proposes a learning-based surrogate model for JCC-OPF with renewable generation. This model equivalently converts joint chance constraints into quantile-based forms. Two multi-layer perceptrons are trained based on special loss functions to predict the quantile of constraint violations and expected power loss. By reformulating these two MLPs into mixed-integer linear constraints, we can replicate the JCC-OPF without network parameters. Two pre-processing steps, i.e., data augmentation and calibration, are further developed to improve its performance. The former trains a simulator to generate more training samples for enhancing the prediction accuracy of MLPs. The latter designs a positive parameter based on empirical prediction errors to calibrate the outputs of MLPs so that feasibility can be guaranteed. Numerical experiments based on the IEEE 33- and 123-bus systems validate that the proposed model can achieve desirable feasibility and optimality simultaneously with no need for network parameters.