I know oysters will eat engine oil, but cooking oil is a different type of chemical so is there any use in adding it to the substrate for growing mycelium?
Vegetable oils are basically triglycerides which are chains of organic compounds with hydroxyl groups.
The use of vegetable oil cakes has been examined in the cultivation of oyster mushrooms. Hydrocarbons are architecturally similar to lignin which is the natural substrate for Oyster mushrooms, and it does not take them long to adapt to this as a food source.
If you want to do this, soak some of your solid substrate in cooking oil to be used as a supplement. And as always, nutrient enrichment increases the risk for contamination.