I used to be able to get up seconds before my alarm went off, but nowadays I have some sleep issues so I definitely need the alarm. During the day, if I'm in a routine I'd probably have a sense of the time but definitely have no sense of time without it. Sometimes an hour has passed in 20 minutes
and sometimes it can take two (hours).
Most likely, I'd survive without it since my Blackberry and I are joined at the hip, but I'm so used to it.