I can't seem to find any information that would indicate whether they had or not. I know there were some American Christian missionaries encouraging the millenarian, and the United States was largely occupied with its own civil war, but is there anything to be noted?
If we set aside the missionaries, the answer is not much of one. Remember that the Taiping Civil War was largely concurrent with the Arrow War in addition to the US Civil War. You had various individual Americans such as Frederick Ward who were there as independent soldiers of fortune (see this post from earlier today for a bit about him), but you didn't have much an active official American presence there otherwise.
There were Americans stationed in the area leading up to the Arrow War, and there were engagements between China and the US at the time, such as the Battle of the Pearl River Forts in the 1850s, but after the limited conflict between the two sides, they went back to peacemaking. The Treaty of Wanxia was only about a decade old at this point, and after the Battle of the Pearl River Forts America took up an official position of neutrality in the conflict between China and Britain.
Most of the significant people involved on the US side to returned stateside for the Civil War if able, and by the time Hong had moved to Nanjing, there was very little official contact on the US side. America was hedging their bets at the beginning. By the end, missionaries and diplomats alike had become irritated with the Taiping government.
There's really not that much to be said about American interaction in an official capacity.