Does sleep in humans re-structure based on the expected sleep time?
I haven't heard of studies like the one you're proposing, but you can test this hypothesis on yourself with this app. 

Knowing you need to sleep less than your usual amount will probably affect the quantity and quality of your sleep, but not because of an "internal clock". Most likely, whatever you need to wake up early for will cause you some anxiety, which will affect both sleep duration and quality.