This paper investigates the use of synthetic face data to enhance Single-Morphing Attack Detection (S-MAD), addressing the limitations of availability of large-scale datasets of bona fide images due to privacy concerns. Various morphing tools and cross-dataset evaluation schemes were utilized to conduct this study. An incremental testing protocol was implemented to assess the generalization capabilities as more and more synthetic images were added. The results of the experiments show that generalization can be improved by carefully incorporating a controlled number of synthetic images into existing datasets or by gradually adding bona fide images during training. However, indiscriminate use of synthetic data can lead to sub-optimal performance. Evenmore, the use of only synthetic data (morphed and non-morphed images) achieves the highest Equal Error Rate (EER), which means in operational scenarios the best option is not relying only on synthetic data for S-MAD.