The magic in MLP doesn't seem like an outcome pump. I suppose it could be set really short-term, so stuff just moving on its own is the only way it can work, but at that point it's just omnipotence. There are things ponies can do and things they can't do, and the difference isn't how likely it is to happen by chance.
I suppose she might not notice this, but if there's going to be a moral here, she ought to be wrong. She's basing her theory on an interesting idea she's heard, not evidence she's seen.
The obvious experiments would be to try and see if ponies are better at things that are more likely and if the most likely result is what happens.
The crossover universe this fic is set in contains some extra items not in the standard MLP universe. One such thing is that gems can be 'charged' with magic, which can be released by anyone as spells, using Latin. (There's a timey-wimey explanation behind how that came to be possible.)
That said - I'm entirely happy for her to be entirely wrong; I just want her to be wrong in the right way, if that makes sufficient sense.
There are two ways to do outcome pumps, one simple and one very tricky, which you might choose between when defining the rules of your universe's magic system. Which one's better depends on what your readers like, and how much trickiness you yourself can handle as an author. The simple way to define it is to say that when you cast a spell, universes that descend from the one in which you cast it are reweighted, but their total weight is preserved. The tricky way would be that the weights are not conserved, which would allow limited backwards causality. For an extreme example, consider Nullus Universus, a spell that sets the weights of all universes in which it's used to zero. It would be impossible to observe such a spell being cast - people would mysteriously decide not to use it, or mispronounce the words, or whatever was the most-probable branch in which it isn't used - but precommiting to cast it if something else happened, would prevent that thing from happening. (Such a spell would almost certainly be lost quickly, though!)
The tricky way would be that the weights are not conserved, which would allow limited backwards causality.
They already have time travel.
In my latest chapter of my ongoing My Little Pony crossover fanfic, "Myou've Gotta be Kidding Me", my protagonist has had a thought. She has discovered that she lives in a universe containing cross-universe travel (which brought her from Earth to Equestria), time travel (which has at least some limits, but can be used for tactical purposes) and magic (of the mana/spell variety). Before arriving there, she read many of the Sequences, even if she hasn't fully absorbed all of their implications, and has been rather busy to think on them very much. I've tried combining all of that by having her posit that the local form of magic is actually a way of implementing outcome pumps, and that the mysterious 'mana' is closely tied to the self-consistency of any given blob of amplitude of quantum wave-functions. My readership seems to generally approve of the technobabble I used
Since this is fiction, I could just as easily have had her posit angels pushing on every electron, and had that be so; but I'm trying to write rationalist fanfiction, and have her strength be in coming up with ideas my readers can use. I haven't made a concrete decision whether or not to have this set of technobabble be the truth for the setting; but I'm at least going to try to use it as the basis for her to try running some experiments to test it. And, in doing so, cover a bit of ground about such things as the difference between Bayesianism and the social organization of the Scientific Method - particularly given that she feels she is under very heavy time pressure to not just get accurate results, but get them quickly.
Might anyone reading this have any suggestions for improvements to the technobabble I've used so far, particular experiments she could try, bits of the Sequences that are worth covering in the process, or anything similarly related?