Probably some standard emulsifier is surely added. That for me would be the key bit: Wikipedia suggests "emulsifier containing refined vegetable oil".
> Ingredients: Fresh Dairy Cream, Sugar, Alcohol, Maltodextrin, Milk Products, Cocoa extracts and flavours, Irish Whiskey, Colouring: 150b, Emulsifier: E471, Acidity regulator: E331
https://en.wikipedia.org/wiki/Mono-_and_diglycerides_of_fatt...
That being said, Bailey’s isn’t that shelf stable and will likely turn into undrinkable too faster than the average veggie oil will go rancid. And veggie oil can be stabilized to some extent by adding vitamin E.