Answer: No. Since this is a McKinney-Vento family, they need to be enrolled immediately, even without the TB test. This is clear in the law:
“The school selected in accordance with this paragraph shall immediately enroll the homeless child or youth, even if the child or youth—
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” (42 USC §11432(g)(3)(C)(i)(I)).
Unless the student is showing active symptoms of a contagious disease, a school cannot deny or delay enrollment while immunization or other health records are obtained.