Exactly. Immigration is actively enforcing the rules now and doing checks on WPs and passports. If you can't produce those on very short order, your ass is going to the detention center.
Working without a WP, especially at a formal school, is a huge gamble, and I would never do it.
Like I said l, I'd rather live in Siberia (with temperatures dipping below -60 °C), or in war-torn Myanmar, than stay in Thailand illegally. It just ain't worth it.