Could a civil war soldier have known about or even read The Communist Manifesto? Any examples of your average solider both union and confederate having read Marx?
Short answer:
Vanishingly small.
Long answer:
After the suppression of the revolutions of 1848, many German liberals and radicals went into exile abroad. Of these, a fairly significant number went to America — in fact, Marx himself considered it, but it didn't pan out and he stayed in London for the rest of his life instead. Some of these exiles could be reasonably expected to know of Marx, if not the Manifesto itself, since the Neue Rheinische-Zeitung (Marx's paper from 1848-1849) was fairly well-circulated and Marx himself was decently famous in Cologne. Many of these exiles had anti-slavery sympathies and ended up joining the Union Army — including Marx's good friend Joseph Weydemeyer, who became an officer.
Furthermore, from 1852 to 1862 Marx was the London correspondent for the New York Daily Tribune, a fairly large newspaper that catered to a Republican audience. A frequent reader of the Tribune would probably be familiar with Marx's name, although probably not his personal or political history.
So Marx was not totally unknown in America, and the few circles in which he was known could be expected to reliably support the Union when the war broke out.
However interesting this may be, though, it doesn't add up to much. The number of people who were familiar with Marx was relatively small, especially compared to the massive amount of people who ended up serving in the Union Army. Those who were familiar likely had very little knowledge of him beyond his writings in the Tribune unless they were German radical exiles; and among those, only some could be described as "followers" or "believers." Marx did have a loyal following among many German communists, but he was hardly the only major figure in the German radical left.
As for the Communist Manifesto: the first run had a limited circulation, and the text was not even published in America until the 1870s, well after the war had ended. In fact, the Manifesto's notoriety really began to rise only after the Paris Commune of 1871, which brought Marx into the public eye as a leader of the International Workingmen's Association (which was falsely accused of instigating the uprising, although Marx made no secret that he was deeply sympathetic to it).
So the average Union soldier would very likely have no idea about Marx, and the few who did still would not have had a strong grasp of who he was. The average Confederate soldier would have even less, since the Tribune was mostly a Northern paper and most German exiles were Unionists. If by some chance they did know of him, however, they would almost certainly not be a follower: Marx was highly anti-slavery and pro-Union, and even wrote a letter to Abraham Lincoln on behalf of the International congratulating him on his re-election in 1865:
The workingmen of Europe feel sure that, as the American War of Independence initiated a new era of ascendancy for the middle class, so the American Antislavery War will do for the working classes. They consider it an earnest of the epoch to come that it fell to the lot of Abraham Lincoln, the single-minded son of the working class, to lead his country through the matchless struggle for the rescue of an enchained race and the reconstruction of a social world.
Not exactly the kind of thing which would be too endearing to the average Confederate.