Answer
No, cooking oils cannot spontaneously form membranes because of the lack of hydrophilic groups. Lipids are nonpolar, whereas water is polar. So lipids float on the surface of the water without blending in water because lipids are insoluble in water.
Work Step by Step
Lipids are hydrophobic molecules, whereas water is hydrophilic. There is no sharing of electrons between water and lipids when they interact. So, when lipids and water are mixed, lipids float on the surface of the water, reducing lipid-water interactions.