Can you study in US high school if entered in country in tourist status?

[MikeW]

I am currently in US under L1 status, and my family members with L2. We have permanent address in school area and kids do go to local schools.
My L1 based employment is ending soon in US therefore believe our Visa's become revoked - if we re-enter to US under tourist Visa can my kids continue in local School e.g. until end of the school year after which we return to home country?
Thank you for your responses!