No no, it isn't that magic is fueled by dead ponies. I haven't seen all of FMA, so I don't know exactly what their explanation for alchemy was, but my idea of magic is basically like this:
- There is magic in the world. It is essentially pure potential energy.
- Magic can become any sort of energy it needs to be be.
- Magic is constantly flowing in and out of every living thing.
- All living things are bound to the 'magical flow'
- ponies can manipulate the magic flow in the world through various means
- When a pony dies their soul returns to he magical flow
- When a soul encounters an empty body (A unborn foal, or a zombie pony maybe), it will enter it, if the body is compatible (so you only rarely get a unicorn soul in a pegasus body, as well as the gender equivalent. It still happens, but it's rare)
from a scientific standpoint, 'magic' is just the most basic form of energy. It fuels everything, up to and including the soul. The magic is alive and works of its own volition to run the world, clustering into frequencies of heat, cold, stuff like that. Certain clusters and bunches of magic in the flow will become a soul, and the clutsers can pick up and drop off other bits of magic between lives. They're not even set solid during life; in life the clusters can be altered depending on how the pony uses it. a pony who delves into magic as deeply as say, Twilight, would gain enough magic and a solid enough control over their personal connection that even after death the soul would remain aware. IT can then learn to more actively harness the magical flow. These such souls are called 'old souls', and can learn to bond themselves to the magic of a single object or place - the old souls then become what are essentially gods. Celestia and Luna, in this fanon, are old souls who bound themselves to the magic of the sun and moon.
So yeah. Magic is just a base expression of energy, and it clusters and flows to become every other kind of energy, including souls. Magic doesn't run on pony souls, pony souls run on magic.