We completed our first umrah here during the night, came back to change, prayed the dawn prayer together, ate breakfast and went to bed. The notion of a sleep pattern is irrelevant to this experience. You sleep when you can, pray when you must, and eat, and read, and chat, and answer e-mails and blog in between.
It was 35 degrees centigrade at 1.30 am, by the way, so avoiding the heat during the day, if possible, is eminently practical. Another good reason to sleep by daylight.