Mine have had to cope like this and whilst we've had a couple of moments with crayons and scissors, mostly it's worked out fine. It has to, they're children to a single mum with disabilities. I can't always be as on top of things as I would like to be.
I don't allow mine downstairs before me, but they can entertain themselves in their rooms until I am fit to get out of bed. I often put a little picnic breakfast, a dvd, clean clothes and some activities in a basket when I feel particularly bad, and they feed themselves, get dressed, brush their teeth and entertain themselves until I get up. Of course I then take some responsibility for any mess they make unsupervised, and we all tidy it together and come downstairs for some lunch and time together.
Have had a few mishaps along the way, but at 6 and 4 now they are starting to get pretty self-sufficient. Bolts on doors is a must to keep them out of the dangerous areas, kitchen being first and foremost, although I personally write off the entire downstairs for mine to keep the animals from being pestered. If they are upstairs alone, my bedroom will have a hook lock on it to prevent access (from tomorrow I hope).
If I had to be awake when DD was every time, I'd have barely slept at all these past four years, she can wake at 2am and start her day there, with no more sleep until 8pm that night. I have had to find ways to cope.