Shouldn't do, if it's mostly fat and oil blocking the drain. Soap has to have free fat, more fat than needed to make the soap. For two reasons, one to stop there being any unspent lye remaining in the soap, and the other as a skin conditioner. The drain cleaner, if it is sodium hydroxide, should heat the fat and oils and turn them into soap, which then should dissolve.
I can't think of any other substances that would end up in the drain that would react with sodium hydroxide in such a manner to create concrete. Maybe if it was a mound of hair and fat. I don't know if the heat would melt the hair to form a hard substance? I don't have much knowledge of hair and how it reacts to high temperatures.