Is it possible to get an education visa for taking online classes full time?

No chance.

You have to enroll/study at a school accredited by the Thai ministry of education.

You normally need paperwork from this ministry (applied for by the school on your behalf) to get an education visa, although with a bit of luck in your own home country you might be able to get said visa without paperwork.

Then, 90 days after your first entry in Thailand, you would need to apply for an extra 90 days at your local immigration office, and to get that you need to show them paperwork showing your class attendance meets the minimum requirement (legally 150 ours/year, practically they want proof of 4 hours/week).

Several private thai language schools (some who are even forum sponsors ) currently offer an ED visa for studying thai and teach the classes online.

To the best of my knowledge the students have no problem securing either their first single entry non-immigrant type-ed visa at a thai consulate in neighboring countries, nor do they have problems getting additional 90 day extensions of stay based on continuing education. The schools which offer this type of ‘distance learning’ are all accredited with the Ministry of Education and provide you with the documentation you need.

It would appear the classes are taught on Skype, and have several students in various locations that log on and then learn together from the thai teacher based at the school. In fact, I've seen it in use at several private thai language schools here in Bangkok.

I'd drop an email to a couple of the schools which have adverts on this forum and ask.