Judging by what we know of reincarnation and how life works in ff14, its certainly possible for reincarnation to happen and for outside processes to interfere- see the dotharl and how the allagan siphon can take away the aether of someone which is what they know is removing oneself from the cycle of death and rebirth.

another dotharl sidequest also goes over one dotharl who thinks he isn't the soul whose name he bears. Turns out he is but was unclear on the exact history of his name. (namely each reincarnation had a preference for a different weapon than the last)

additionally the buduga also comment that had they would happily wait for a xaela wol to be reborn as a man had they been a dotharl. So at least two tribes there think its possible.

We also have at least 2 examples of reincarnations: the player and the one revealed in eden.


tldr: its possible, but new life does get formed as well