Stearic Acid is a weak acid, so it would react if placed in contact with an aqueous solution of a base such as HCO3-
or even with H2
0 alone as per other weak acids. The *rate of reaction* might be a lot slower (so you would not see it react right away) in some circumstances than you might expect between say a small molecule of acetic acid and bicarbonate ion due to the fact that the stearic acid molecules would not be free to diffuse anywhere in solution like acetic acid since their long chain fatty acids would tend to form membranes (of course you can always disrupt the formation of those membranes, so this would be situation specific).
KMnO4 is an oxidizing agent. It typically can either cleave or oxidize fatty acids, and its behavior is heavily dependent on the pH. There are many journal articles on these topics. Here is an example of a journal article for potassium permanganate oxidation of olefins:http://www.springerlink.com/content/u45u627p77431380/