It's specifically the Treaty of Nanjing that your question refers to, as the Unequal Treaties is the name given to a series of treaties over the course of many years, the Treaty of Nanjing being the first and that which was signed at the end of the First Opium War.

Certainly those living in one of the treaty ports (Shanghai, Ningbo, Xiamen, Fuzhou, as well as Guangzhou) would have been immediately aware of the treaty, as would people in Nanjing, or anywhere else where the war was visible. Word travels fast, and at least in these areas people would have been witnessing changes both from the end of hostilities as well as the actual effects of the treaties (such as the appearance on the scene of British citizens replacing the Cohong (gonghang 公行) system of international trade.

You have to keep in mind that the loss of the Qing to the British forces was a really big deal, and it contributed significantly to a general feeling that the Qing was losing control. The average aside from the most disconnected of rural farmers would have been quite aware of these kinds of shifts that were going on, and even for those in more rural areas, there was a sort of trade network for information from the bigger cities. A loss to the hairy barbarians would have been a significant piece of news that would have spread blazingly fast.

edit: You might also be interested in the book A Chinese Account of the Opium War which is available in full on archive.org as it's out of copyright. It's often attributed in English to EH Parker as though he were the author but it's actually Parker's translation of a Chinese text by a guy named Wèi Yuán.