Ohio has always been ahead of the game in terms of online charter schools. I was traditionally homeschooled for the better half of my academic career. My brother went through junior high and highschool using various online solutions. From my understanding, no one was a big fan of ECOT. They provided severely underpowered machines, which were in fact locked down too much. At the time, their bureaucratic setup was confusing and stifled learning. It may have gotten better in the years since, but I can't recommend it based on what I've seen.
Following up on that, my brother also did two years with OHDELA. They had their act together much better than ECOT, but again, issued terrible hardware. This time however, it was a crummy iMac locked down even tighter than the Compaq mini towers ECOT gave out. Furthermore, OHDELA relied far too much on trying to simulate a traditional classroom. Mandatory chatrooms and timed virtual blackboards just got in the way of the original promise of working at your own pace. It may have benefited those that needed the help, but making it compulsory did more to slow my brother's progress than anything.
His final time was spent with an organization called Buckeye Online. They provided a fairly decent laptop computer (completely open!) and relied more on bookwork. This was exactly what my brother had wanted all along. He wasn't chained to a desk or required to participate in some simulated blackboard environment. All he had to do was read the chapter in his text book and then submit the corresponding lesson electronically. He blew through the material and graduated one year earlier than he would have otherwise.
Now again, a lot has probably changed since I watched my family work with these different organizations. Some may be better or worse than they were. Some of the points of contention that my brother had may be the exact thing that your child would prefer. The point is to study up on them before just blindly signing up. Most of them do offer seminars leading up to the traditional start of the school year. Go and listen, ask questions, discuss your concerns. It has been my experience that you'll usually have the ear of some of the more important people within the organization.
So can students be home-schooled electronically? Absolutely. I would say that the benefits far outweigh any negatives. Most of the perceived problems that people have with homeschooling can be quickly and easily remedied if you're not a lazy parent. Having an online support system, as provided by these institutions, definitely makes things easier. It's still not something you can just throw and your child and expect to happen. It's a framework for the parents to work within, to help out, to expand upon, and to monitor. Of course, any parent who takes their job seriously would be doing that anyway, even if their child went to a physical school.