Except in the degenerate case of a single photon.
But you still have the problem though that whilst 4-vectors are well-defined in the tangent spaces, except in the Minkowskian case, there’s more than one way to define equivalence classes of 4-vectors in a decently sized hypervolume of spacetime.Plus there’s no guarantee that all defitnitons of equivalence classes of 4-momentum will lead to it being a conserved quantity.
Obviously in the case of a satellite orbiting a planet your generally well within the Newtonian limit and there must be some sort of functional conservation of momentum that can derived from a full general relativistic treatment. I’m not saying the same isn’t necessarily true of a single photon passing the planet, but the photon is highly relativistic so it doesn’t seem trivially true that there will be a sensible functional conservation of momentum.
The qualifier you’ve added isn’t neccessary, it doesn’t matter which direction the flashlight is pointed, the light will not escape to infinity.