The idea of an unlicensed school would find opposition on two fronts. First, the economic and political clout against it would come, of course, from the NEA. Like so many other organizations that seek to secure their monopolies with gratuitous licensing requirements, the teacher's union will scream (in true Mrs. Lovejoy fashion) "Please, won't someone think of the children?" But the arm of that clout will be expressed, of course, by the government. Between NCLB and just the general idea of Outceom Based Education, the government will insist that all students be subjected to testing to prove that they meet minimum education requirements. Failure to agree to (and comply with) this requirement would be met not only with potential jail time (for which participants would be presumably prepared) but also child neglect charges and the removal of children from homes - for which the participants are very unlikely to be prepared. Such actions have already been taken, though there has been some success against that in the courts. But a concerted government effort would, I think, be ultimately far too costly to the movement to sustain it. To comply with the testing requirements, OTOH, would be tantamount to licensing.
You also mention businesses which do not withhold. Jail time is a given, but more to the point the IRS would move immediately to seize the assets of such businesses and/or their employees. A means of possible avoidance would be to pay estimated taxes up front, but that, again, negates the point of the exercise.
Even given the courage of participants faced with incarceration, how many are willing to tear their families apart and give up their homes and other assets? No doubt some would, and such things may generate sympathy from the public to some extent. But not, I think, very much. It is one thing to rally behind a people held in bondage for centuries and unable to do something as simple as eat at a restaraunt or use a bathroom because of skin color. It's another thing to feel sorry for people who have to send their kids to school and pay taxes.
In the end, such ideals would be viewed by most as at best overzealous and at worst dangerously cultish. No doubt a lot of people would be sympathetic to the basic idea of standing up to the government, and even more to the idea of controlling your own kid's education. But public education and the idea of taxation are ingrained in the public psyche. The cause would seem more like political grandstanding, not like the noble stands taken by Ghandi and King. In the end, I think such gestures would be neither successful in the short term nor meaningful in the long run.
