Can my US wife accompany me on an Education visa in Thailand even if she isn't taking classes?

You could get a 90 day single entry ED visa from a thai consulate in the US before you wing your way here by enrolling in the school and having them send the documentation to you in the US

AND

if you did that your wife could get a 90 day single entry Non-O visa at the same time by being married to someone who is getting an ED visa to study here.

Now whether she could get that 90 days extended inside the country is debatable. I have not seen people successfully get their spouses matching extensions when the other person is studying at a private school only for real university courses.

I'd say contact the school you'll be attending and ask them what they suggest you do.

IF they can't offer any suggestions, she could always get a 6 month METV <- multi-entry tourist visa. That would give her almost 9 months of stay here (in 60 day increments).

There is no 6 month ED visa :O

Your wife would need to get her own visa.