What I saw this old, old, old, old taiwanese lady do was she fried everything else together, and once the fried rice was done she moved all the rice to the sides of the wok so that the middle was exposed, she poured in a little oil and added a beaten egg mixture, she flashfried it for about 20 seconds and then she mixed it all up again. Best fried rice of my life. The egg was not coating the rice, but it was incorporated in the fried rice.