Education

No.  That would be giving false or misleading information on the FAFSA form

FAFSA form page 8 - https://studentaid.gov/sites/default/files/2021-22-fafsa.pdf

If you are the parent or the student, by signing this application you certify that all of the information
you provided is true and complete to the best of your knowledge and you agree, if asked, to
provide information that will verify the accuracy of your completed form. This information may
include U.S. or state income tax forms that you filed or are required to file. Also, you certify that
you understand that the Secretary of Education has the authority to verify information
reported on this application with the Internal Revenue Service and other federal agencies. If
you electronically sign any document related to the federal student aid programs using an FSA ID
(username and password) and/or any other credential, you certify that you are the person identified
by that username and password and/or other credential, and have not disclosed that username
and password and/or other credential to anyone else. If you purposely give false or misleading
information, you may be fined up to $20,000, sent to prison, or both.

This is a FAFSA question, not a tax question. You should look for help on the FAFSA web site or call the contact number.

I'm not sure which question on the FAFSA you are concerned about. The FAFSA doesn't ask about dependents with the same meaning as dependents on your tax return. It asks "How many people are in your household," including "your children, if you will provide more than half of their support. . . ." That's a different requirement from claiming a dependent on your tax return. You can claim a child (under 19 years old) as a dependent on your tax return even if you don't provide more than half of the child's support. Conversely, providing more than half of the child's support does not necessarily entitle you to claim the child as a dependent on your tax return. So your daughter could be a person in your fiancé's household, according to the FAFSA definition, even if he cannot, or does not, claim her as a dependent on his tax return. Whether someone is a person in your household for the FAFSA, or a dependent on your tax return, are two different questions with different criteria. You would have to figure out who provides more than half of your daughter's support. If your fiancé does provide more than half of her support, then she would count as a person in his household under the FAFSA definition, and counting her would certainly not be false or misleading.

That's how I understand the instructions on the FAFSA. But I still suggest that you check with FAFSA if you want to be sure.