Some preliminaries
What you describe is modeled pretty accurately by the Jaynes-Cummings model. This is a model used a lot in quantum optics to describe the emission and absorption of photons by two-level systems (e.g. atoms, in good approximation) in a cavity. Therefore, for simplicity, I'm going to assume that our atom and the photons are in an (optical) cavity.
When we start with a two-level atom in the ground state and exactly $n$ photons$^1$ in a mode which is resonant to the transition between the ground state and the excited state of the atom, the Jaynes-Cummings model tells us that the whole system will undergo so called Rabi oscillations. In our example this means that the atomic population varies periodically between the ground state and the excited state, while the photon number varies periodically$^2$ between $n$ and $n-1$.
The Rabi oscillations describe stimulated emission and absorption. If we start in the ground state with $n$ photons, wait until the atom is in the excited state and then make a measurement, we observe (stimulated) absorption. If we start in the excited state with $n-1$ photons, wait until the atom is in the ground state and then make a measurement, we observe stimulated emission$^3$. Note that those two processes are described by exactly the same formalism, the only difference is between which points in the Rabi cycle we make the measurement.
Time reversal
So having discussed the framework which we need to accurately describe stimulated emission and absorption, what are their respective time reversed processes? Well, the time reversal of a Rabi oscillation is again a Rabi oscillation, just going in the backwards direction. So what was stimulated emission before (excited atom and $n-1$ photons $\rightarrow$ ground state atom and $n$ photons) becomes (stimulated) absorption (ground state atom and $n$ photons $\rightarrow$ excited atom and $n-1$ photons) and vice versa! So to make a long story short, the time reversal of stimulated emission is exactly the same as absorption. Therefore they are of course indistinguishable. In particular, the time reversed process of stimulated emission is far from hypothetical, every time you observe absorption, you might say that you witness the time reversal of stimulated emission.
Finally, as to the question whether all $n \rightarrow n-1$ processes look the same: They do in the sense that, again, all those processes are described by the same framework and are conceptually the same. However, the Rabi frequency, which is the frequency of the Rabi oscillations, grows with the photon number. That means that the time it takes for the system to change from a state with the atom in the ground state and $n$ photons into a state with an excited atom and $n-1$ photons takes less time if there are more photons at the beginning, i.e. if $n$ is bigger. In that sense, the transition from the ground state to the excited state during the absorption process is faster if there are more photons.
Tl;dr: The time reversal of stimulated emission (starting with $n-1$ photons) is exactly the same as absorption (starting with $n$ photons). The process of absorption with photon numbers $n \rightarrow n-1$ only depends on $n$ in so far that, in a certain sense, the transition is faster for higher $n$.
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$^1$Note that in general the state describing the electromagnetic field is not an eigenstate of the photon number operator, such that usually there isn't even a well-defined "number of photons". States which are eigenstates of the photon number operator are called Fock states and are in fact quite difficult to produce experimentally.
$^2$When you do the calculations, it turns out that (at least at certain times) the atomic state and the state of the electromagnetic field are entangled. For example, you might get a total state like $|\psi \rangle = \frac{1}{\sqrt{2}} \big( |g\rangle \otimes |n\rangle + |e\rangle \otimes |n-1\rangle \big)$ where $|g\rangle$ and $|e\rangle$ are the ground and excited state of the atom, respectively, and $|n\rangle$ is the state of our electromagnetic field mode containing $n$ photons. This makes sense intuitively, because when we measure the atom in the ground state, it follows that the atom didn't absorb a photon, which means that there are $n$ photons, whilst if we measure the atom in the excited state, it follows that the atom did absorb a photon, which means that there are $n-1$ photons.
$^3$We have ignored spontaneous emission here, and I don't want to go into detail on this topic, just note that we can in principle extend our model to incorporate spontaneous emission as well. In that case we get dampened Rabi oscillations.
