Your body has many clocks that are tied to the Earth. I don't travel a lot so I don't know how they reset or how fast, but there are a lot of body cleaning activities that go on between 10pm and 2am. I am most familiar with one because of the reflux I had. Between the listed hours, the stomach produces a lot of acid, it is thought it is to clean itself. I read here about a similar cleaning cycle in the liver at that time.
One thing I noticed with daylight savings is that my stomach acid-producing period switched between 10pm and 2am to 11pm and 3am, and it did not adjust back until daylight savings ended. So it was not fooled! :)
Does it mean that these things won't get cleaned if you're awake? No, but I would guess it isn't as effective a job done.