This exactly. Try for yourself. Personally I find myself more creative when I don't use caffeine - being slightly tired may even help a little. However, being slightly tired does not help with my more normal, non-creative, work.
A former coworker was just the opposite - put a few espressos in him and the creativity almost oozed out.
A former coworker was just the opposite - put a few espressos in him and the creativity almost oozed out.