When a natural disaster occurs, humanitarian organizations need to be prompt, effective, and efficient to support people whose security is threatened. Satellite imagery offers rich and reliable information to support expert decision-making, yet its annotation remains labour-intensive and tedious. In this work, we evaluate the applicability of convolutional neural networks (CNN) in supporting building damage assessment in an emergency context. Despite data scarcity, we develop a deep learning workflow to support humanitarians in time-constrained emergency situations. To expedite decision-making and take advantage of the inevitable delay to receive post-disaster satellite images, we decouple building localization and damage classification tasks into two isolated models. Our contribution is to show the complexity of the damage classification task and use established transfer learning techniques to fine-tune the model learning and estimate the minimal number of annotated samples required for the model to be functional in operational situations.