In 1994, one team of Swedish researchers set out to answer the question by having a group of 10 people consume a few drinks on two separate days.
In one case they drank after an overnight fast, and in the other, they drank after they ate a modest breakfast.
On the day the subjects ate, the rate of intoxication was slower, even though the amount of alcohol had not changed. But the subjects also reached significantly lower blood-alcohol levels over all - on average about 70 percent of what they were on the day they skipped breakfast.
Source: NY Times
Of course, once it's absorbed into the bloodstream, eating won't get it out faster :)