Sadly, no. The really scary thing about World War One is that not only did people march cheering to sign up and get slaughtered, on the actual battlefield they marched head high in close order and in several cases wearing pretty gaudy and colorful uniforms right against massed rifle fire, machineguns and artilery barrages. Many cavalry forces in all seriousness did not even carry rifles.

The results are well known, and at least the basic lessons were learned inside the first six months or so. As you can imagine both contemporaries and today's historians were and are fairly interested in how such bloody and utterly wasteful stupidity was even possible.

One reason I've seen cited is sheer pig-headed romanticism of the higher officer corps, the last refuge of the decaying military aristocracy, who could not mentally accept the idea that modern war was a war of machines and men operating like machines, not of heroes, individual valor and dramatic cavalry charges. Plus the poor schmucks had been raised up and conditioned to a severely idealized and romanticized version of Napoleonic warfare (the sort of idea involving rearing horses and severe-looking heroic officers in impresssive uniforms you see in old paintings) and actually hadn't experienced a major war fought with modern weaponry firsthand.

Both the Crimean War and the Franco-Prussian War had been fought more or less by the old methods and weaponry, and between those and the Great War there were little but colonial brushfire wars whose lessons were, in the spirit of the arrogant racism so prevalent during the Age of Empire, not assumed to apply to "white" armies. Or, the machinegun might be fine for mowing down angry natives and Ethiopian dervishes but surely Western soldiers would be of better stuff...

The American Civil War seems to have been a fair bit more modern in character, in many occasions involving extensive field fortifications and trenchworks as well as (primitive) automatic weaponry, so it's perhaps not that surprising they learned at least some of the lessons sooner. Plus the sabre was of little use fighting Indians - most cavalrymen left theirs at the base when going out, for the thing was just extra encumberance and a general pain in the butt.