That's the sort of thing that will depend on how the dice rolls go.
Of course. But the zone between "safe from our mountain because it's in the citadel's shadow" and "far enough away from artillery to be safe" is going to be very narrow if it exists at all, and crucially, the orcs
don't know about the mountain to know they need to thread that needle.
Odds are that they'll charge at Karagril, the place they see as theirs and home to those ratties they want to take revenge on, instead of fruitlessly rushing at the sheer cliff that is the approach to the Citadel, but the potshots we take at them may cause them to switch their primary target to the Citadel.
Either way, whichever they charge at, they'll be exposed to artillery on the approach. Being quite wise in the ways of applied brutality, they'll very quickly grasp that rushing in single file isn't going to cut it, so they'll park outside of the artillery and wind up for a knockout punch.
It's hypothetically possible that some amount of them will poke at the other mountains while this is happening, although it's not
that likely due to the lack of an obvious fight, with Zilfin being the primary contender on account of some of them potentially wanting to tussle with a dragon.
It seems unlikely to me that these piecemeal efforts will make any significant progress on mining open the entrances to those mountains if they occur at all - if by some stroke of luck they
do manage to pry Zilfin (or Yar, or Mhonar) open before enough of them accumulate for the rush on Karagril or the Citadel, it should be obvious to Mathilde due to the theatre level movements swiveling towards that peak, so we'll just fire the Eye early and thus buy time to re-seal the mountain.
Otherwise, if things go as I'd expect them to, we should wait to fire the Eye right for when the first mass attack on Zilfin or the Citadel launches that we don't expect to be easily turned away by the artillery.
If we're very, very unlucky, this should still buy enough time for ~25% or so of the enemy force to be in the killzone, and has decent chances of decapitating their leadership. Effectiveness goes up from there on better rolls.