It is possible and fairly easy if you have a shop and are not mobile.
If you are mobile, you have to deal with a few issues.... You would have to enter all the phone-called-in and prescheduled appointments into the same calendar people are scheduling with online. You wouldn't want someone scheduling an appointment online at the same time as an appointment you have already scheduled via another method.
The other thing to deal with is the timing of the appointment. Two appointments may be scheduled back to back. But they may be on opposite sides of town. If someone called and scheduled something like that over the phone, we would put in some time to allow us to travel from place to place. But if these two appointments were scheduled online, you don't have the opportunity to screen for this.
People who schedule appointments online don't nec take that appointment very seriously. So you may spend time driving to a location only to find out that the person is no longer available as they promised. That would be really frustrating!
I am working with a friend to put together a site that allows online scheduling. It also will have secure online payment so people can prepay if they would like. It'll all be accessible to me on the road from a PDA with an aircard. I will also be able to process credit card transactions on the road with that pda...
SC~