I don't know the age, but I do remember being like "I can make time disappear!"
I don't have any such dramatic stories about waking up days later though that I recall. I mostly realized I could retreat into an inner world and hours/days would fly by as long as I lived there.
According to my parents, I also swore that I'd sometimes go to bed in one house & wake up in a different house (my parents were divorced). I don't remember this, and I don't remember if I actually said it was days later or not.