No, 2 eggs do not contain enough protein for optimal muscle protein synthesis following a workout. According to the Academy of Nutrition and Dietetics, the optimal amount of high-quality protein for muscle protein synthesis post-workout is 20-30 grams [1
]. The average large egg only contains 6.5 grams of protein, so if a person were to eat 2 large eggs, this would leave them short by 7-12 grams [2
That said, this protein shortfall could be easily made up by combining 2 eggs with 2 pieces of whole-wheat toast, which would provide an additional 7.2g of protein as well as carbohydrate for replenishing muscle glycogen. Find more information on post-workout nutrition needs here
 Thomas, D. T., Erdman, K. A., & Burke, L. M. (2016). Position of the Academy of Nutrition and Dietetics, Dietitians of Canada, and the American College of Sports Medicine: Nutrition and Athletic Performance. Journal of the Academy of Nutrition and Dietetics, 116(3), 501–528. https://doi.org/10.1016/j.jand.2015.12.006
 Bjarnadottir, A. (2017, January 26). How Much Protein in an Egg? A Detailed Look. Healthline. https://www.healthline.com/nutrition/protein-in-egg#TOC_TITLE_HDR_2.