Darkin use Void based blood magic to perform flesh weaving. So the immediate effects of a Darkin's corruption can only effect blood and flesh. However, prolonged exposure to blood magic can corrupt magically, mentally, and spiritually... Probably. Even Aatrox doesn't know if his corruption is due to his immortal essence being bound to a weapon, or the effects blood magic eventually took on his mind and soul, and their connection to the Void.
So humans, yes.
Yordles, eventually, granted a yordle with nothing to do eventually becomes corrupted and evil on their own, so adding a Darkin would only quicken that process.
Vastaya, yes, they are mostly spirits, but they still have flesh.
Vasthayshai’rei 
, maybe, but I think they would need to want it.
Ghosts, same as the Vasthayshai’rei, but I think the Mist trumps the corruption of the Darkin. Plus the Mist makes them a ghost, they could just get out of the sword at that point.
Ascended, yes, that is what caused this problem to begin with.
Aspects, yes, because their host body is made of flesh. So, say, Morgana or Pantheon picks up a Darkin, it will eventually win, but that does not mean they will keep their celestial powers. Cause, you know, the celestial can take them away.. at least in Pantheon's case.
Celestials.... I wanna say no, but in Soraka's case, where they take on a physical, fleshy, form to enter the physical realm, possibly. So for Soraka, yes, for Bard and Aurelion Sol, no. Can't flesh weave a man made out of a horn or a ghost that is juggling suns.
Iceborn... Uh... Well their flesh is frozen, and they are already linked to Lissandra who is in turn already linked to the Void.... I don't know.
Voidborn, no, they invented fleshweaving.
) can push through their influence.