Yes, K1 is technically a non-immigrant visa, but it is processed as an immigrant visa. Hence, CEAC status is shown via the CEAC IV link up to the interview stage. After that, CEAC status for K1 typically moves to the NIV link.
CFO is required for all emigrating PH passport holders, including those intending to fly out with K1 visa. If the BI officer at the airport sees the K1 visa in the passport, they will demand to see a CFO sticker or certificate. If your fiancee has neither, she will not be allowed to board the plane. Unless your fiancee is a senior citizen, she must attend the CFO seminar to obtain the certificate.