You should always have it. When it comes to anything thai govenment use the better to have it and not need it than to need it and not have it rule. That said the nice ladys that check the documents before you get your second ticket have justbasked me where I am staying and written it for me in thai. Never needed tm30. American Passport.
While I havent seen it yet at my school, from what I understand all the schools have a "meh" class that they shove the ed visa riders into. Wherever you do end up going just make sure when you go to sign up you let them know you are serious about learning Thai and intend to be there every class and they should make sure you dont get put in their meh class.
they do all the paperwork and meet you at immagration to help if there is any questions during extensions. I get in person classes 3 times a week. I know they have some online students as well but not sure if those students are on ed visa.