No,
If you are a US citizen, Permanent resident or eligible non citizen you cannot apply for institutional aid by just filling out the CSS profile with out the FAFSA
Emory Financial Aid states:
Need-based applicants typically receive some combination of institutional and federal grants, loans, and work-study awards. To be considered for need-based financial aid, you must submit the FAFSA, CSS Profile, and tax returns (if applicable) by the stated deadline for your admission plan.