Well, without worrying about any of the niceties, the de Broglie
wavelength
of the elephant is surely extremely short, so in the classically allowed
region it does not exhibit any observable wave behavior, and in the
classically forbidden region its wavefunction has an exponential
fall-off
with a very short characteristic distance.
As far as macroscopic objects exhibiting qualitatively different
behavior,
I don't buy it based on my experience in the
sort-of-microscopic/sort-of-
macroscopic world of nuclear physics -- but maybe my intuition isn't
reliable for the generalization to elephants! When, say, two lead
nuclei fuse at an energy below the coulomb barrier, it's 100% valid
just to treat them using the Schrodinger equation for their
center-of-mass
coordinate. There was also a note in a recent Physics Today about
double-slit interference patterns and suchlike for buckyballs.