I found this article:
http://news.nationalgeographic.com/news/2005/12/1219_051219_drunk_elephant.html
They doubt it for several reasons:
But the first flaw in the drunken-elephant theory is that it's unlikely that an elephant would eat the fruit if it were rotten, Morris says.
Elephants eat the fruit right off the tree, not when they're rotten on the ground, he explained.
"This a largely self-evident fact," he said, "since elephants will even push over trees to get the fruit off the tree, even when rotten fruit is on the ground."
And considering how heavy an elephant is, it would take a lot of alcohol to get them drunk. As the same article says:
This raises another question: Even if, under very peculiar circumstances, an elephant were exposed to alcohol, how much would it take to get it drunk?
Through calculations of body weight, elephant digestion rates, and other factors, the study authors conclude that it would take about a half gallon (1.9 liters) of ethanol to make an elephant tipsy.
This article also debunks the myth.
Abstract
Africa can stir wild and fanciful notions in the casual visitor; one of these is the tale of inebriated wild elephants. The suggestion that the African elephant (Loxodonta africana) becomes intoxicated from eating the fruit of the marula tree (Sclerocarya birrea) is an attractive, established, and persistent tale. This idea now permeates the African tourist industry, historical travelogues, the popular press, and even scholastic works. Accounts of ethanol inebriation in animals under natural conditions appear mired in folklore. Elephants are attracted to alcohol, but there is no clear evidence of inebriation in the field. Extrapolating from human physiology, a 3,000-kg elephant would require the ingestion of between 10 and 27 L of 7% ethanol in a short period to overtly affect behavior, which is unlikely in the wild. Interpolating from ecological circumstances and assuming rather unrealistically that marula fruit contain 3% ethanol, an elephant feeding normally might attain an ethanol dose of 0.3 g kg(-1), about half that required. Physiological issues to resolve include alcohol dehydrogenase activity and ethanol clearance rates in elephants, as well as values for marula fruit alcohol content. These models were highly biased in favor of inebriation but even so failed to show that elephants can ordinarily become drunk. Such tales, it seems, may result from "humanizing" elephant behavior.