Answer: Yes, you are correct. The applicable language from the McKinney-Vento Act, as amended by ESSA, states:
“(C) IMMEDIATE ENROLLMENT-
(i) IN GENERAL.– The school selected in accordance with this paragraph shall immediately enroll the homeless child or youth, even if the child or youth—
(I) is unable to produce records normally required for enrollment, such as previous academic records, records of immunization and other required health records, proof of residency, or other documentation; or
(II) has missed application or enrollment deadlines during any period of homelessness.
The citation is 42 US Code section 11432(g)(3)(C). So if this student is appropriate for the magnet school, and the school has space, missing the lottery cannot be a barrier to his immediate enrollment.