No, I can't sleep with CI on.... I must have absolute silence to be able to sleep.
But there has been times that I would fall asleep on the couch while watching TV/Movie with CI and I don't wake up unless there was a loud noise from the TV. Sometimes I fall asleep on the plane and the engine won't bother my hearing while I have CI on.
But about 99% of the time, I must have absolute silence to go to sleep, to be able to be in deep sleep. Or otherwise, every single noise whether it's soft or loud, it wakes me up.
All my life, I've been sleeping with no sounds so it's like its only way I'm able to sleep.... no sounds at all.