What do you need to shut down that requires GFCI?
If it is not 15/20 amp 120 volt cord and plug connected, it usually will not require GFCI. Not much goes under a hood that is 120 volt that requires being shut down by the fire suppression system. Gas appliances may have 120 volt supply but usually with gas appliances all that is required is to shut down the gas when fire suppression is activated.
If you were to go by NFPA 17A which deals with wet chemical suppression systems you'd be correct.
"4.4.4.1 On actuation of any cooking equipment fire-
extinguishing system, all sources of fuel and electric power
that produce heat to all equipment protected by the system
shall be shut down." [emphasis added]
However, most jurisdictions deal with the IBC and the IBC requirements have a quirk in them requiring:
"[F] 904.11.2 System interconnection. The actuation of the
fire suppression system shall automatically shut down the
fuel
or electrical power supply to the cooking equipment.
The fuel and electrical supply reset shall be manual."
So one requires the electricity to shut down
only if it produces heat (the more sensible option in my opinion) and the other require
any electricity to equipment under the hood to be shut down.