Are you implying that the stimulation from Diet Coke is much less than the stimulation from the fear or anger for fight?
No, just elaborating on the caffeine, cortisol and fat connection.
I really doubt a diet coke is going to kick off the cortisol response to any extent.
However, taking 600 mg of caffeine in fat burner tabs plus your typical daily intake of coffee, coke and daily stress would elevate cortisol.