No, but that’s because the Cream Egg is the wrong sort of thing to try and add, you’re taking an item that is already going to feel very fatty on the mouth and adding a shed load more fat (plus a ton of sugar). It would destroy the balance.
What might work is maybe changing some of the standard acidic components (gherkins, mustard, ketchup, tomato, onion) for something that also brings that level of acidity. It’s partly why people started adding pineapple to burgers and gammon, although imho they are generally too invasive a flavour. Get too much balance and you start to destroy the umami flavours that really make the dish sing.