The answer to your question is yes, they did use something like modern rifle squad tactics, but different given the weapons, etc. As was mentioned in previous post, it is encoded in the "Instructions for Skirmishers" in the infantry tactics. All infantrymen were instructed in both the close and skirmish order tactics during the war.
When a company, or regiment, deployed as skirmishers, the company's two platoons were divided into two sections each on the skirmish line. The captain remained in the rear of the skirmish line, and the platoons (half-company) divided into two sections (quarter-company) under lieutenants or NCOs who were very much in charge of their sections when on the skirmish line. More, in deploying as skirmishers each two files from the 2-rank line (four men), or group of four, acted as "comrades in battle." No matter the extension or gap called for between these groups, the four men always remained five paces from each other, always alternated their fire, between front and rear ranker...
And when firing while advancing each pair of front and rear rankers were to alternate their fire and movement... First the front rank man of every file halts, fires, and reloads before "throwing himself forward." The rear rank man of the same file doesn not stop but continues to march, and passes 10-12 paces beyond his front rank man, halts, comes to a ready, selects his object, and fires when his front rank man has loaded (throws himself forward).
When firing in retreat they fire and move alternately in a similar manner. By this at least half of the skirmishers were to be loaded at any given time...
1. The movements of skirmishers should be subjected to such rules as will give to the commander the means of moving them in any direction with the GREATEST PROMPTITUDE.
2. It was not expected that these movements be executed with the same precision as in closed ranks, nor was such considered desirable. Such an exactness would have materially interfered with their prompt execution of the movements.
3. When skirmishers are thrown out to clear the way for, and to protect the advance of, the main corps, their movements should be so regulated by this corps, as to keep it constantly covered. When not acting with a main corps; they are not regulated by such but by their own circumstances.
4. To that end, every body of skirmishers should have a reserve, the strength and composition to vary "according to circumstances."
To greater or lesser degree these tactics were employed throughout the war, even in the major battles. Pickett's charge, for example, had a "heavy" skirmish line advancing in front of it by the Union descriptions.
Most of the fighting in the Atlanta Campaign employed skirmishers on the picket lines of the armies...where they remained any period of time the men dug out foxholes for themselves, and connected them to the others of their groups to form what they called "rifle-pits" etc. At the Battle of Utoy Creek Sgt. Ives of the 4th Florida notes the skirmishers' rifle pits were 30 feet apart. These were always in front of the works constructed by their reserve, or the line of battle further in rear (which many rebs called "ditches")...
Historians generally ignore this skirmishing by not describing it, but many veterans memoirs have excellent descriptions of incidents on the picket lines... Attacks by the lines of battle can be more easily "imagined" and become the subjects of artwork and movies (skirmish lines being largely invisible when not shooting) but many veterans of the campaign noted the skirmishing between the picket lines in front was continuous, exhausting, and frequently deadly.
In line of battle, Civil war commanders would launch assaults by units in close order "en echelon" in order to fix the enemy defense and then moving another unit forward, etc. For example, in his division's attack on the Snodgrass hills at Chickamauga Sept. 20 afternoon, Gen. William Preston CSA advanced Gracies' brigade in front, and several minutes later Kelly's brigade on his flank to strike the enemy in front of Gracie in flank by obliquing right....
In fact, as i recall, Bragg's whole plan at Chickamauga on the 20th was a large scale, en echelon attack from right to left...