No, neither side hired mercenaries in the American civil war. Foreign mercenaries were loathed by the American people being specifically cited in the U.S. Declaration of Independence as one of the injuries and usurpations of King George III against the colonies. Hiring foreign mercenaries would be a suicidal act by either government.

Alternatively, mercenaries were most useful in wars where the numbers of soldiers on a side were compartively small. The U.S. Civil War featured hundreds of thousands of soldiers at arms on each side. A few thousand Hessians would be a drop in the bucket. The Union had no shortage of manpower, and the Confederates lacked the seapower to safely get a mercenary force to its shores, and never had the ability to fully equip the forces it could raise internally. So it never made sense to hire mercenaries.

The confederates liked to characterize the Irish and Germans fighting for the north as "mercenaries", but the Irish and Germans though of themselves as fighting a war in order to earn the respect as American citizens. Irish and Germans were treated with contempt like our current South Asian and Mexican populations in the USA. The war allowed the Irish and Germans to have the social mobility following the war.

I think there was a case of where The Confederates less than hired more recruited some Australians from Melbourne. Could be wrong however. I remember reading about it some where. http://en.wikipedia.org/wiki/Australia_and_the_American_Civil_War