Conserved quantities like energy are characteristic of time-reversible dynamical systems.  Conway's Game of Life is a dissipative, non-time-reversible system, and thus not likely to have any nontrivial conservation laws.

In fact, I can't even think of any invariant boolean properties preserved by the CGoL update rule:

- "There are live cells" is not an invariant property, since patterns can die.
- "There are finitely many live cells" is not an invariant property, since even infinite patterns can die.
- "There are exactly four live cells arranged in a 2x2 block" is not an invariant property, since other patterns can turn into a block.
- "There is no [Garden of Eden](https://conwaylife.com/wiki/Garden_of_Eden) pattern" is not an invariant, since a GoE can be present in the first generation (but will never be present in any later one).
- "There is no [orphan pattern](https://cp4space.hatsya.com/2022/01/14/conway-conjecture-settled/)" is also not an invariant, since even orphans can die if disrupted from the outside.

In principle, a cellular automaton rule _could_ have non-trivial invariants, such as a "[superstable](https://mathoverflow.net/questions/132687/is-there-any-superstable-configuration-in-the-game-of-life) orphan" pattern that can neither be formed unless it is already present on the lattice nor destroyed if it is.  But as far as I know, no such patterns exist in Conway's Game of Life (nor would they seem to be quite what you're looking for, even if they did exist).

There are, of course, trivial invariants based on the eventual evolution of the pattern under the iterated CGoL update rule, such as "this pattern will eventually die."  (Incidentally, I'm also pretty sure that this property, and others like it, are computationally undecidable — it should be possible to construct a pattern in CGoL that will simulate a Turing machine and die out if and only if the machine halts.)  But a conserved property that can only be calculated by simulating the system for an unbounded number of steps is hardly useful for doing physics with.