I don't believe the printer will wake and clean itself. The printer seems to have 3 basic ways to set this up.
1. check every print. Does an ANC before every print. Possibly useful for large production house producing a large job of large prints that isn't watched very closely. This could be used along with the number of attempted auto cleans to basically stop the print job if nozzles failed during the run. Not really very practical other than perhaps that situation.
2. Check occasionally. Not a bad option, and as you mentioned not sure what "occasional" is, but more applicable when printing a large job, it will check occasionally during the job.
3. Manual, don't auto check. unlike previous printers which this option effectively eliminated all ANC other than when switching blacks, this simply disables 1 and 2 above. The printer will still do an ANC when powered on after having been shut down for a period of time or if it's been asleep for an extended period of time, and when you switch blacks. It seems this is somewhat timer based but I really can't figure out how much time or if there are are other variables as to when this happens.
Originally I turned the printer off when not using it, but I thought leaving the printer powered on would avoid power on auto checks, which it doesn't. It seems this is more like a timer based function of some kind (and not affected by the timer clean settings which I have set to off). If it's been off or asleep for a period of time it will still execute a nozzle check.
On the positive side, ANC's rarely trigger a clean with my printers, and seems to be more accurate in that I'm not getting false positives and the printer dropping into an endless cycle of check/clean, check/clean like previous generation printers seem prone to do. The x900 series improved this (other than the 4900), but my p5000 and p9000 rarely need a clean, when they do it's usually only a couple of channels and one clean always seem to do the job. I moved about 2 years ago, and I no longer keep a humidifier in the room like I did with my 9900. Humidity in the winter is below 30%, maybe as little as 10-20% here in Utah with forced air heat, but hasn't been an issue.
For a while now I've been leaving mine on all the time, my p5000 goes to sleep after one hour but I don't have it turn off and that seems to work fine. It will check nozzles if it's been asleep for a day or so. My p9000 is set to sleep after 15 minutes, and turn off after 4 hours. It rarely does either. The p5000 is USB and if I unplug the cable it will wake up. the p9000 is ethernet, and so my guess is something in the network seems to keep the printer awake. Sometimes I do find it is asleep, and then will hear it wake up on it's own. Haven't really tracked down the cause.
Neither seem to have an issue with missing nozzles regardless of whether I turn it off or let it sleep, or in the case of the p9000 leave it running all the time. I'm probably going to get back in the habit if turning them off when not using them, since leaving them on doesn't seem to gain me anything.
