No such version of the 1950 original screen version exists.
Mary Chase [the writer] had the idea that film audiences should actually see Harvey at the end of the film because she "didn't want anybody to go out of the theater thinking Elwood is just a lush. He believes in Harvey...and I think the audience ought to believe in Harvey, too."
The studio reportedly considered this and experimented with how to show him to the audience, including his appearance in silhouette, and even by attaching a rabbit tail to the taxi driver at the film's conclusion. In the end, however, the studio won out and wisely decided NOT to ruin the illusion.
Only once had a giant rabbit actually appeared on stage in the play of Harvey, and the results were disastrous. Theatrical Producer Brock Pemberton recalled in a 1945 interview that at that performance in Boston, "a chill descended on the gathering, which never quite thawed out afterwards."
As far as I can tell, Harvey only appears in a portrait painting:
The movie was remade for TV in 1996 but I apparently Harvey does not actually appear in that version either.
The ending scene in the 1996 differs from the 1950 original.