My daughter attends a school along this model. There is no computer lab and no wi-fi. The facts that children need to master and the skills of logic and rhetoric are not technology-dependent. That having been said, a classical home-school program could probably be conducted quite well over the Internet, but the technology is not the content; it is merely a vehicle for delivering content, in the same way that a book or an instructor might be. Too much of the high-tech appliances I saw in my daughter's first (public) school was actually edu-tainment and/or babysitting.
Yes, in the upper grades students use computers for writing papers and for some research, but they don't use them in the classroom.