Models that embed graphs in non-Euclidean spaces have shown substantial benefits in a variety of contexts, but their application has not been studied extensively in the biological domain, particularly with respect to biological pathway graphs. Such graphs exhibit a variety of complex network structures, presenting challenges to existing embedding approaches. Learning high-quality embeddings for biological pathway graphs is important for researchers looking to understand the underpinnings of disease and train high-quality predictive models on these networks. In this work, we investigate the effects of embedding pathway graphs in non-Euclidean mixed-curvature spaces and compare against traditional Euclidean models. We then train a supervised model using the learned embeddings to predict missing proteinprotein interactions in pathway graphs. We find large reductions in distortion and boosts in indistribution edge prediction performance from using mixed-curvature embeddings and their corresponding graph neural network models. Furthermore, mixed-curvature modeling provides some utility for out-of-distribution edge prediction.