No! Caffeine is a drug that excites the nervous system and it therefore uses energy. The lift from it is beause you are "borrowing" cellular energy that you can ill afford. However sleep works, it is obviously a restorative mechanism involving energy metabolism. The proof of its drug effect is that people often get withdrawal headaches.
Agree w Dr. Lonsdale. Because coffee doesn't restore what was missing - sleep. Sleep deprivation can ^ risk for fatigue, irritability, v concentration, diminished memory, ^ infection rate, ability to tolerate stressors, blurring of vision, v energy level, ^ micro-sleeps, weight gain, exacerbation of psychiatric problems and can even lead to psychosis.