The question can obviously only be entertained in a philosophical sense. But I think it an interesting idea to ponder. Even an oscillating model of the universe might have a constant Eall
If Eall isn't constant, is it increasing or decreasing, and where is the energy coming from or going to? If there's another "Where" that gives or takes energy from our universe, then I would contend that our model of our universe is incomplete to the extent that this other "where" is currently excluded.
So, say we incorporate "otherwhere" into a fresh, new model of "the universe" and, to avoid doing this recursively, further suppose that all existing successive "otherwheres" are also likewise incoporated. Now, redo the calculation of Eall Do we NOW have a constant or a variable?
Aw, Geez!
Can I talk to the other guy again?
Just kidding. Your point is valid. If not all energy is accounted for, it could be intruding from, or escaping into, an otherwhere.
That doesn't make a difference. The Universe is like an ocean, (only more so!), if a little rain evaporates from the Atlantic, and falls into the Pacific, what difference does it make?
In anything as large as a Universe, there will be leakage, both in and out. That doesn't mean there is as much as one additional Universe, but there could be a Universe of Universes.
That still doesn't change it. In your question "Is EAll a constant or not?" the answer is "not." Mostly it increases. In some circumstances it could decrease.