Yes. The artist certainly appeared to be copying the uniform of the Berdan sharpshooters of the US Army, with green uniforms, and leather leggings, hair-on cowskin knapsacks, etc.
The First Georgia Sharpshooters of the Confederate army as a battalion formed in the summer of 1862 from men of several different units combined. For example, Company A, 1st Georgia Volunteers (Olmstead's regiment) was transferred/detached to serve as Company B of the new 1st Battalion of Georgia Sharpshooters, etc. Company A of the Sharpshooters was composed of men transferred from the 1st, 25th and 47th Georgia Volunteers, etc.
Uniform clothing was contracted for the battalion by the Government, from Mr. Henry Lathrop of Savannah. Though it was noted that by the time they went to the front not all of the men had been outfitted. Some wartime ads from Mr. Lathrop's concern...
From July, 1862:
View attachment 547195
View attachment 547196