Cooking oil lipids consist of long, unsaturated hydrocarbon chains. Would you expect these molecules to form membranes spontaneously?

No, because they do not have a polar end to interact with the water phase.

Explanation:

When the molecule of a lipid has a strongly polar group in addition to the hydrophobic hydrocarbon chain it is said to be an amphipathic lipid. They are schematically represented as one or two straight or broken lines (representing hydrophobic hydrocarbon chains), ending in a circle (representing the hydrophilic polar head).