No, a day hike to Whitney will not acclimate you to that high altitude at the end of that flight. The topic of acclimatization has been frequently discussed on this forum, but you may have missed some of that discussion. If you could spend several days at high altitude and then take that flight soon after, before your acclimatization wears off, then you might have some advantage over the other passengers.
A day hike to the summit of Whitney might give you some idea how you might feel when stepping off the plane, but that's about all. Acclimatization to high altitude takes at least several days, if not longer, and begins to wear off fairly rapidly after returning to low altitude.
Check this out, especially the topic "Travel to altitude":
http://www.altituderesearch.org/
