Not according to William Deresiewicz:
If food were really a narrative medium, then all food would be narrative, just as the clumsiest and most simplistic story is. If food were really a narrative medium, it would also be able to speak about anything, to whatever degree of detail and specificity you want—not just, as with the curry, itself. Any made object can, in that sense, "tell a story," but only about its own making. A tall, green-eyed astronaut fell in love with a lawyer who recently lost her job: when you can cook me a dish that says that—and tell me how you’d change it if the astronaut were dark instead of fair—then we can talk about food as a narrative medium.
Food is ordered: but so are spreadsheets, or even regular sheets, when you make your bed in the morning. Food evokes emotions: but so do sunsets, or train sounds, or the cigarette smell of a bar. Food embodies ideas: but so does everything that’s made. To evoke is not to represent, and to embody is not to express.