I don't see any way that they could sleep without being hooked up to breathing machines, given that one generally loses control over voluntary functions with unconsciousness. Perhaps one could train oneself to have some sort of surface-level sleep, like those who can sleep standing up or the descriptions given by soldiers of learning to sleep while marching. Of course, I'm not sure how such a training process would be conducted, under the circumstances.
But the day time is actually, for me, a more interesting question. If we posit that the person would experience all of the normal discomfort associated with holding ones breath when they forgot to breathe, then they might be able to function. Should they forget to breathe, they would be alerted to the fact in plenty of time to take a deep breath without any real adverse effects; their breathing might be more sporadic, but there's no reason to assume that it wouldn't get the job done.
After a certain amount of time, I think it would become an automatic function of its own- not in the sense that the brain stem would handle it, but in the sense that every thirty seconds, the person would remember to take a breath so that it became a part of their daily rhythm. I wonder if that would interfere in any manner with higher brain functioning- having to have a basic point on one's mind constantly, like they say that having to remember a three digit number impairs mathematical ability, etc. It's even possible that the person would prefer to be hooked up to the automatic devices to avoid the trouble of remembering, although this is somewhat dubious considering the degree to which such machines impair ones freedom.
Of course, the person could never fall asleep accidentally, since we've pretty much determined that that would mean stopping breathing. This, though, I don't consider such a huge limitation on freedom, compared to the other stuff, but that could be because I tend not to fall asleep until I have given myself 'permission' to do. In any case, it would probably be wise for the person to have some sort of device monitoring oxygen levels and emitting a loud alarm before they become dangerous, since the unpleasant sensations of holding one's breath might not be sufficient to wake the person up in time.