Good question Catherine. Usually after I eat a big meal I feel sleepy. This doesn't happen after a sandwich, but otherwise I start looking for a comfortable chair. So, eating is useful but not always the best if I have a lot of work to do.
Hunger may not be so useful by itself, but a lot of hunger i.e. fasting is supposed to be powerful if you know what you are doing. I haven't really fasted myself but one of my professors was saying that in the ancient world it was common to fast as a way of getting clarity before a big decision. There are apparently places in the Bible where this happens, and in other sources. So maybe if you know how to do it, it allows you to think better. This idea has not really survived to modern times though, might be interesting to think why.