Previous posters are correct- distance is not a factor for LAC, so they could apply from the FC's address and still obtain a place at the school near their new family, even if this is hundreds of miles away.
Should the adoption fall through, the child should not be disadvantaged. As they will still be LAC, for the purposes of admissions, they will be an 'excepted child', and therefore do not count towards ICS regulations. They could make a late application, and the chosen school should go over numbers and admit them. This is also the case for children adopted from care (or leave care under a Special Guardianship or Child Arrangement order)- however, should the school decide not to offer a place, a LAC is in a slightly better position than an adopted child, as the LA which looks after them can direct the admissions authority of a school for which they are not the admissions authority to admit the child.
Confusingly, if the school is an academy, then the Secretary of State is the only person able to direct the school to admit the child- and here, provision is made for adopted children. I can find nothing in writing which refers specifically to LAs directing other schools to admit adopted children, even though they too are 'excepted'. I hope this means that children adopted from care are being admitted to their chosen schools, but I suspect that many are being refused places and adoptive parents have not been made aware of their status as excepted children, so do not challenge the decision.
Put simply, If the child is living with FCs in January, they and the SW should apply for a place at the school near their adopted family; they should obtain a place.
If the adoption breaks down for any reason, the FC and SW can make a late application to a school near the FCs, and they should obtain a place, even if this is via direction. LAC should not be placed on waiting lists.