I've only managed to complete this quest in LH 0.85 so apologies if it is different in FE.

Previously, I've never managed to find both dragon eyes quest statue (Q: Would the AI start/complete it) but had all 3 spawn near my starting point in a recent LH game. I was actually quite surprised to discover that the quest to find the 2 dragon eyes did reward you with the Ashwake dragon when you have obtained said eyes, instead you had to battle three high level dragons together.

My question is... given how powerful your army needs to be to take on three dragons concurrently successfully (much less take on three dragons without suffering massive losses), well, why would you still bother doing the quest then? Probably said army is powerful enough to win the game by conquest or the Master Quest, and if not, a Level 1 Ashwake Dragon to replace all the troops you lose fighting three high level dragons will not make enough of a difference to matter (although admittedly the Fire Immunity of the Ashwake dragon makes it a good tank against the Master Quest boss).

Also, not sure if it is a known issue or intended, but in LH 0.85, you can postpone on fighting the dragon trio. The issue is that the prompt asking you to fight will then keep repeatedly popping up non-stop after almost every action (including things such as Designing Units). The quest is "At the Dragon Gate" if I am not wrong.