No. All children in the United States have the right to a free public school education in the school district in which they live. Regardless of your immigration status, if your child has a disability and meets special education eligibility criteria, she is entitled to the special education services required by her IEP. [Plyler v. Doe, 457 U.S. 202 (1982).]
Immigrant children do not need a “green card”, visa, passport, social security number, or any other proof of citizenship or immigration status in order to register for school. You do not have to and should not check with the immigration authorities before sending your child to school. It is illegal for a school to require you to do so.
It is also important that only those children who are in need of special education services receive them. Special education law requires that testing for special education eligibility and services take language and cultural factors into consideration. [34 C.F.R. Sec. 300.304(c); Cal. Ed. Code Sec. 56320.]