There is no cream of any kind in carbonara. The starchy pasta cooking water mixed with the other ingredients creates an emulsion that is creamy but for sure I would never add cream I don't want to discourage you but pasta carbonara can be a tricky one to make. You have to get it just right so the eggs don't scramble.
And although pancetta or guancale is traditional, bacon is just fine if that is all that you can find.