517.34(A)(5) allows it. I would ask your fire official if he requires it.
Quote
517.34 Equipment System Connection to Alternate Power Source.
(A) Equipment for Delayed Automatic Connection. The following equipment shall be permitted to be arranged for delayed automatic connection to the alternate power source:
(5) Kitchen hood supply or exhaust systems, or both, if required to operate during a fire in or under the hood.
There is the same language in 517.43(A)(4) (Health Care Facilities)