As most sleep professionals know, the answer to this question is no. However, this article on IO9 goes over some interesting studies that have attempted to answer this question, including one that sought to determine if banking sleep in anticipation of sleep deprivation works.

To summarize: Your body must have sleep. Full stop. As of 2014, there is no strong evidence that a person can condition his or her body over time to require less sleep. “The fact is,” says Mitler, “when we look at well-rested people, they’re operating at a different level than people trying to get by on 1 or 2 hours less nightly sleep.”