The assessment of left atrial appendage (LAA) thrombogenesis has experienced major advances with the adoption of patient-specific computational fluid dynamics (CFD) simulations. Nonetheless, due to the vast computational resources and long execution times required by fluid dynamics solvers, there is an ever-growing body of work aiming to develop surrogate models of fluid flow simulations based on neural networks. The present study builds on this foundation by developing a deep learning (DL) framework capable of predicting the endothelial cell activation potential (ECAP), linked to the risk of thrombosis, solely from the patient-specific LAA geometry. To this end, we leveraged recent advancements in Geometric DL, which seamlessly extend the unparalleled potential of convolutional neural networks (CNN), to non-Euclidean data such as meshes. The model was trained with a dataset combining 202 synthetic and 54 real LAA, predicting the ECAP distributions instantaneously, with an average mean absolute error of 0.563. Moreover, the resulting framework manages to predict the anatomical features related to higher ECAP values even when trained exclusively on synthetic cases.