We investigate to what extent mobile use patterns can predict -- at the moment it is posted -- whether a notification will be clicked within the next 10 minutes. We use a data set containing the detailed mobile phone usage logs of 279 users, who over the course of 5 weeks received 446,268 notifications from a variety of apps. Besides using classical gradient-boosted trees, we demonstrate how to make continual predictions using a recurrent neural network (RNN). The two approaches achieve a similar AUC of ca. 0.7 on unseen users, with a possible operation point of 50% sensitivity and 80% specificity considering all notification types (an increase of 40% with respect to a probabilistic baseline). These results enable automatic, intelligent handling of mobile phone notifications without the need for user feedback or personalization. Furthermore, they showcase how forego feature-extraction by using RNNs for continual predictions directly on mobile usage logs. To the best of our knowledge, this is the first work that leverages mobile sensor data for continual, context-aware predictions of interruptibility using deep neural networks.