Can a generative adversarial network (GAN) be used for data augmentation (i.e. to generate synthetic examples that are added to a dataset)? Would it have any impact on the performance of a model trained on the augmented dataset?
Yes, GAN can be used to "hallucinate" additional data as a form of data augmentation.
See these papers which do pretty much what you are asking:
If your GAN is sufficiently well trained, there's no reason why this shouldn't help improve model performance. If your GAN is bad, you'll get garbage.
After long time, I would conclude the answer is no, based on some quite solid theoretical basis https://en.wikipedia.org/wiki/Data_processing_inequality
For visual tasks, data augmentation can often be accomplished by rotation, scaling, or rearranging patches. These transformations do not necessarily add information, but can be useful for models to learn to generalize better.
The generator in a GAN learns a complex distribution from its training data from which you can sample, and you can view these new samples as another type of transformation of the original data, akin to rotation, scaling, etc.