I would have thought that at the levels we're talking about, noise as such does not really cause fatigue.
If anything, a bit of low-level, expected and familiar noise will help you to go to sleep.
When you're asleep, you're not totally unconscious.... Sudden unexpected noises, or even the sudden stopping of a familiar noise (dare I mention engine noise?) are quite capable of waking you up.
Active noise cancelling becomes relevant when the noise level is such, that it actually causes fatigue, or otherwise interferes with the work you're doing.
It seems to make little sense in a CRC.
I would far prefer the iPod idea, with an under-pillow loudspeaker so you're not bothered by the earpieces or the wire.
Put on something you like, something relaxing you enjoy. Listening to it will then drown out your perception of other noises, and should send you to sleep in no time.
Maybe I am underestimating the problem, since I rarely have trouble going to sleep? At one time, a few years ago, I did, so I just listened to one or the other of my favourite cassettes.... I never heard them to the end.
CJ