The Communist Manifesto probably had no impact. It wasn't a terribly influential text initially and might be seen as only one expression of the discontent behind the Revolutions of 1848, were it not for the document's subsequent history. By the 1860s, the Manifesto was basically out of print and unavailable, although it was subsequently revived by labor movements in the later 1800s.

Marx, however, might have had a direct impact through his other writings. At the outset of the Civil War, Marx regularly contributed to various newspapers as a correspondent based in London. As an economic observer, he was uniquely poised to diagnose the Southern dedication to slavery as the true cause of the war, and his voice held special authority as an outsider. We might compare Marx to the op-ed writers or political commentators of today. Readers might take Marx as an unbiased observer (yikes!), they might already know Marx and his agenda, or they might have only a vague idea about the leanings of the papers he published in.

At any rate, Marx helped spark the conversation that the Civil War was truly a war about slavery. Fort Sumter had been attacked in April 1861, the First Battle of Bull Run was fought in July, and by October, Marx was arguing to readers in New York that they needed to confront the issue of slavery head on:

The war has not been undertaken with a view to put down Slavery, and the United States authorities themselves have taken the greatest pains to protest against any such idea. But then, it ought to be remembered that it was not the North, but the South, which undertook this war ... by loudly proclaiming “the peculiar institution” [i.e. slavery] as the only and main end of the rebellion. It confessed to fight for the liberty of enslaving other people. (The American Question in England, New-York Daily Tribune, Oct 1861)

This appears to have been his first published opinion on the matter. Marx also spread these opinions internationally. In November, he published in the Austrian newspaper Die Presse, as part of a series of articles that he and Engles would republish as a book:

The attempts of the Confederacy to annex Missouri and Kentucky, for example, against the will of these states, prove the hollowness of the pretext that it is fighting for the rights of the individual states against the encroachments of the Union. ... One sees, therefore, that the war of the Southern Confederacy is in the true sense of the word a war of conquest for the spread and perpetuation of slavery. (The Civil War in the United States, Die Presse [pdf], Nov 1861)

Although many Northerners initially saw the purpose of the Civil War to be the preservation of the Union, even at the expense of prolonging slavery, Marx contributed to a rising chorus of voices that the war could not be won without ending slavery as well. The eventual fruits of this realization were the Emancipation Proclamation (1863) and the Thirteenth Amendment (1865).

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For selections on slavery from Capital, as well as the Tribune article, see this pdf. For an analysis of Marx's attitudes toward American slavery, see this pdf.