Simple answer is no. The individual soldier had to pay for his image. Photography was in it's early years there was considerable expense involved to have ones image made. It was unaffordable for most soldiers. Also, more Union soldiers had their image made than Southern soldiers. The supplies for making images were harder to obtain in the South after the war started. Many of the Southern images are pre-war or very early war. There are many CW images of both sides existing that are unidentified.

There are several sites that have collections of CW images available for viewing and for sale. A google search for Civil War Images will find them for you.