Deep learning has shown great promise for fast reconstruction of accelerated MRI acquisitions by learning from large amounts of raw data. However, raw data is not always available in sufficient quantities. This study investigates synthetic data generation to complement small datasets and improve reconstruction quality. An adversarial auto-encoder was trained to generate phase and coil sensitivity maps from magnitude images, which were combined into synthetic raw data. On a fourfold accelerated MR reconstruction task, deep-learning-based reconstruction networks were trained with varying amounts of training data (20 to 160 scans). Test set performance was compared between baseline experiments and experiments that incorporated synthetic training data. Training with synthetic raw data showed decreasing reconstruction errors with increasing amounts of training data, but importantly this was magnitude-only data, rather than real raw data. For small training sets, training with synthetic data decreased the mean absolute error (MAE) by up to 7.5%, whereas for larger training sets the MAE increased by up to 2.6%. Synthetic raw data generation improved reconstruction quality in scenarios with limited training data. A major advantage of synthetic data generation is that it allows for the reuse of magnitude-only datasets, which are more readily available than raw datasets.