A college can offer whatever financial aid it wants. Whether or not it covers the gap between CoA and EFC depends on the college. Note also that many colleges that do promise to cover the gap between CoA and EFC (“meet full need”) calculate their own version of EFC which may be different from the FAFSA EFC (and the EFCs that other colleges calculate).
Parents and students of current juniors should be running college net price calculators for each college under consideration to get financial aid estimates. If need-based financial aid is not enough for affordability, the student needs to seek merit scholarships and/or choose colleges where list price CoA is affordable.