No, the CFI must hold ratings for the category, class (and type if required) on their pilot certificate and category and class on their CFI certificate.
61.193 Flight instructor privileges.
(a) A person who holds a flight instructor certificate is authorized within the limitations of that person’s flight instructor certificate and ratings to train and issue endorsements that are required for:
(7) A flight review, operating privilege, or recency of experience requirement of this part;