it wouldn't be a resonance supplied by the horn driver that would be the source, it would be from the fact that low frequencies (that tend to be omnidirectional) would serve to excite a cavity resonance but for the size/volume of your horn compartment i'd hazard it would likely be be higher in frequency and at"war" volume not likely audible.
Years ago I put an omni measurement mic in that cavity to see what was actually happening in there as we were using dozens of open-backed HF cabinets and the on-stage crew were concerned (for feedback reasons).
There was no prominent peak in the LF band and the several that were there were excited more by the backline instruments cabs on stage instead of the PA itself.
The cavity is occupied by a horn and large driver essentially breaking it up into 4 wedge-shaped regions that were too small to "grab" any of the LF from the PA. The mids were highly directional and you couldn't even tell they were on from behind them when outdoors so none of them were getting in there.
It was only when drums, keys and guitar fired up that the mic picked up anything significant that would peak -and they were far drowned out by the backline itself and the resonances from their open-backed cabinets bouncing around backstage.
We stapled a "placebo" pad of carpet underlay to the inside top of the cavity just to show the stage crew that we took care of the "problem"
