Psychologists have done studies and found that students that take online classes have less retention of the material. http://www.ion.uillinois.edu/resources/tutorials/overview/weaknesses.asp
There is also the issue of academic integrity which can not be ensured on the computer, whether someone is doing work for them or they are cheating. It puts a lot more responsibility on the student and if they do not write things down then they will not remember it as well.
But leaning more towards the no side.
I did home schooling (online based) for the last three years of high school, and I found it much easier to grasp the concept of some things, and my lessons got straight to the point.... No effing around like in person teachers tend to do. For instance, if I was say learning something on fractions, once I proved I understood it, I was allowed to move on.
But, the things I didn't understand I had a hell of a time figuring out. Even though I had real people to email and call, it did no good because I'm a visual learner. Eventually I got lazier, started sleeping until afternoon, and soon I just stopped doing the work, because no one was on my butt about doing it, whereas "real" school, you have someone on you to get things done.
Less papers, and for those who have bad handwriting can type anything on the computer. My school has been providing assignments on their websites and we can type most of our essays on there rather than having all of that paper in our binders. We also receive updates on our grades through a website that lists what we turned in and what we didn't.