The idea of a 'fixed' FoH EQ is that it has supposedly been set up by a pro with sound analysis gear to ensure the response to the room is as flat as possible.
I reality, in many 'community' structures, unless it's actually locked away, it gets tweaked by someone different every week, because they think they can make it sound 'better'.
Once that's been done for a year or two, there's little semblance of the original curve, so it will need doing over from scratch.
The antithesis of that is it becomes like some kind of holy relic, to never be touched by anyone for fear of the wrath of 'the powers that be'. So over the years, someone buys new speakers or amps, but never changes the FoH EQ. It sits there like some ancient talisman whose true purpose is now long-forgotten, fixing an EQ which no longer exists; has completely changed since it was last set properly, because no-one dares touch it.
You're not going to be able to fully compensate for the room just using the board's EQ, but if the FoH EQ isn't tuned to the room precisely, then locked away, then frankly your guess is as good as mine as to whether it will sound better with it or without it.
You really ought to get the EQ fixed/replaced & have the room measured again; then lock it down.