While I didn't notice an immediate difference, it was only a couple of weeks for me before I felt noticeably better back when I first started CPAP (2000). It was always mask issues that caused me to quit using my CPAP, not the lack of results. Like hhopper, when I got my current mask (end of October) I felt significantly better after just a couple of days.
I'm not a doctor, but I question how much "debt" there can really be. I mean, if the CPAP is working as it is supposed to at the right pressure and with no leaks, I don't see how continued tiredness could be attributable to OSA after the first few weeks. Obviously some people continue to be tired, but I've always wondered if they didn't have something else going on as well in addition to OSA (central apnea? narcolepsy?). But again, that's just my uneducated speculation on the subject.