Tactile sensors are increasingly integrated into dexterous robotic manipulators to enhance contact perception. However, learning manipulation policies that rely on tactile sensing remains challenging, primarily due to the trade-off between fidelity and computational cost of soft-body simulations. To address this, we present ETac, a tactile simulation framework that models elastomeric soft-body interactions with both high fidelity and efficiency. ETac employs a lightweight data-driven deformation propagation model to capture soft-body contact dynamics, achieving high simulation quality and boosting efficiency that enables large-scale policy training. When serving as the simulation backend, ETac produces surface deformation estimates comparable to FEM and demonstrates applicability for modeling real tactile sensors. Then, we showcase its capability in training a blind grasping policy that leverages large-area tactile feedback to manipulate diverse objects. Running on a single RTX 4090 GPU, ETac supports reinforcement learning across 4,096 parallel environments, achieving a total throughput of 869 FPS. The resulting policy reaches an average success rate of 84.45% across four object types, underscoring ETac's potential to make tactile-based skill learning both efficient and scalable.