First just think about it in css style: Color: #232323 in comparsion to rgba(X,X,X,0.2). There are more characters to compile in the dom tree. More characters in the dom tree result in heavier loading time.

Second like Geffrey mentioned. In the color only example the browser just got two colors to calculate and to render. In your alpha example it has to calculate a third color. At first the background color than the alpha color that lies above and than the combined color of them two. I think there is no case studie needed, it is just logic.