I'm not sure of the High School situation and distance learning online in the US; reading the thread, I assume that each state has different requirements.
For what it's worth, I teach at college, and I have done a fair bit of teaching to adult "second chance" students. Over the past four years I have taught on an online programme and I have to say that it is extremely useful for people who are attempting to juggle exceptionally busy lives - who have jobs, mortgages, families, bosses, partners, children, pets, commutes, etc. It allows for flexibility in education and it is particularly useful for adults seeking career change, or "second chance" education, because it allows them to study while getting on the rest of their (often quite stressed) lives.
For High School, or normal 18 year old undergrads, I'd recommend it, too, but maybe not to quite the same extent. When I was a student, one of the features of college that I really liked most was the social life, the endless coffees, talking, meeting people. If you are sociable, perhaps, online classes can be difficult, as the social aspect is considerably less pronounced.
Academically, I wouldn't see a problem, as such schools (if they are any good) have good academic and technical support.
Good luck and cheers