I have heard varying reports of "wake-up time", and do not know if it is a result of the headphone charging up, or the amp warming up. I have heard reports of instant charging, and I have personally heard one pair of headphones not wake up until 7:30 (I actually didn't hear them wake up until days later). Anyone at one of Hirsch's early Rockville meets can attest to this (I believe Justin was there, as were canman and taylor). In hindsight, I'd say they were defective, but they sounded fine once they woke up.
So I say: suit yourself. Experiment. Listen to them cold (E.G. after being off all night), listen to them half an hour in, listen to them after being on for four hours. If they really don't sound any different, then I wouldn't leave them on all the time. If they take more than four hours, I'd get another pair. I just don't have that kind of patience (or the desire to pay those kind of electric bills and replacement parts bills -- because you will "use up" that amp faster as a result of keeping it on all the time).