Did the Telegraph significantly influence the course of the US Civil War?

There is an argument among those of us who study the evolution of Operational Art of where it began. It generally splits into two camps with a third minor one. The first two are the 1) American Civil War proponents, and 2) the Napoleonic Wars proponents. First, understand that prior to either of these, the concept was for two massed armies to meet on a battlefield and conduct one large fight (or not depending on parlay) to decide the victor. This is GROSS oversimplification. With the Civil War, both sides still looked for this elusive grand battle which would signal the end of the opposition. From McClellan's failed siege of Richmond to 2nd Manassas and Gettysburg there was this feeling that one battle could end it all if only one side could destroy that army en-mass. The evolution of single battle wars to multiple, simultaneous and sequential battles (Jackson's Shenandoah Campaign is a good example), or what we now call operations heralded the era of Operational Art. This could not have been accomplished without a small number of technological inventions. First, the telegraph allowed a commander to be far removed from battle and communicate with multiple subordinate generals. Unlike the past where a king or a prince had to command all his units in a line of sight with flags and music, the commander could be far removed and command multiple armies. This allowed the control of multiple formations across as much space as you could run a telegraph wire and keep it from getting cut. These usually ran along another invention which changed the nature of movement at the time: the railroad. The railroad enabled a commander to deploy forces rapidly along multiple avenues of approach to converge on a single point where the battle was to take place (external lines of communication). It also allowed for movements of troops laterally...quickly. Changing the way commanders thought about the velocity of war. A third invention is the rifle and the repeating rifle. At the beginning of the war, nearly all Confederate troops carried their own smooth bore muskets into battle. These were highly inaccurate weapons unless you were within 100 yards, and even then had to be fired en-mass to gain effect. The introduction of the rifled barrel and the minie-ball changed the way infantrymen could be used on the battlefield. Neither side used this last one well because the doctrine of employing a Division/Corps/Army on the field was ingrained from the use of the musket for so long. The telegraph was a huge part of the advent of Operational Art and changed the way we could conduct warfare, but it was only one of a handful of inventions which were spawned by warfare at the time. I didn't even get into cannon upgrades at the time.

Absolutely. Theres a few great scenes in the movie "Lincoln" that capture the use of the telegraph.

Much like the radio influenced shipping lanes and eventually WW1. Technology!