I have eaten 4000 calories of fat in an afternoon, mostly in cream and butter as part of a giant poundcake trifle [0]. I didn't throw up but I really regretted it all evening. This was at a time when I was very active and eating around 7000 calories a day.
Supposedly, this works if you eat fat and protein with very limited carbs, if any. For instance, I would gag if I had to eat those sticks of butter by themselves, but I can easily eat a lot of slices of cake. This all is the basis of a ketogenic diet, kind of like Atkins on steroids