Well the thumb isn't a good site as you use it constantly and it has more nerves aka sensitivity than the other fingers. Otherwise, yes you can draw blood from it. As for the little finger, I use that site all the time as it has the least sensitivity for me. Remember when testing to use the SIDES of your fingers, not the ends or the pads. Again, this is simply because there aren't as many nerve endings here and it won't hurt as bad. if you use the new BD Ultrafine III (33G) lancets, you probably won't feel a thing as they are sooooooooo tiny!!!
But to get back to your question, you can use all your fingers anytime, its just that with your thumb constantly in use, its probably not a good place to put a hole!!!