Human gaze data offer cognitive information that reflects natural language comprehension. Indeed, augmenting language models with human scanpaths has proven beneficial for a range of NLP tasks, including language understanding. However, the applicability of this approach is hampered because the abundance of text corpora is contrasted by a scarcity of gaze data. Although models for the generation of human-like scanpaths during reading have been developed, the potential of synthetic gaze data across NLP tasks remains largely unexplored. We develop a model that integrates synthetic scanpath generation with a scanpath-augmented language model, eliminating the need for human gaze data. Since the model's error gradient can be propagated throughout all parts of the model, the scanpath generator can be fine-tuned to downstream tasks. We find that the proposed model not only outperforms the underlying language model, but achieves a performance that is comparable to a language model augmented with real human gaze data. Our code is publicly available.