That is very hard to tell, particularly since your talking about a war that occurred 100 years prior. We only know so much about the parties involved. I also suspect that Ala Mhigo wouldn't have ended up conquering all of Eorzea. Annexing Gridania would have probably been as much as they could have managed while still protecting their northern border. After all they would have still had to hold Gridania in the wake of that which might have gotten difficult if the Elementals had become troublesome. Taking Ishgard, and Limsa would have been a much harder task as Ala Mhigo wasn't a great naval power and they would have needed to defeat Limsa at see to get their armies across the strait and Ishgard was already highly fortified and questionably worth the trouble. Ul'dah would have been quite the prize but would have time to build up substancial mercenary forces as well as potentially make deals with Ala Mhigo's enemies in Ilsebard. Added to that, Ul'dah fights very dirty. The last war they had they turned their enemy army into Zombies.
If Ala Mhigo had had the military strength to pull it off, its hard to say. Again, it would come down to who was in charge. Conquest is rather a jerk move regardless, even though in Ala Mhigo's case there was economic drivers forcing their hand. Manfrid seemed to be more interested in securing viable lands to keep Ala Mhigo from going into decline than building an empire. Also Culturally the difference probably wasn't as severely different. Certainly not the same but the social and religious structures were definitely more in line with their Eorzean neighbours.