As messed up as it is, do you think that the Slaver’s Bay and its people can survive without the institution of slavery? If I remember correctly their land was left all but infertile by their Valyrian conquerors and they import most of their goods from other lands. If they are left with nothing to export, how can they expect to get life sustaining goods in return?

Well, let’s start with the point that a society that can’t survive without the total dehumanization of six-sevenths of its population shouldn’t.

But to actually answer your question, yes I think they can. 

First of all, you’re not remembering correctly. The Meerenese coastland where the cedars were got eroded, but inland there are tons of farms and landed estates which feed the cities, especially along the Skahazadhan. And even if the soil was poor, there’s ways to fix that – better irrigation, better fertilization, anti-eroision planting and reforestation. There’s also a good bit of manufacturing – copper and salt mining, weaving, brick-making and pottery, etc. There’s plenty of commerce in things other than human beings. 

Second, you can’t trust Galazza Galare. In addition to maybe being the Harpy, she’s part of a whole invented culture that exists to legitimate and naturalize the slave system that was created in the Century of Blood. She’s a damn liar trying to sell Dany on the idea that Meereen has no other option than slavery, just like the liars in our own history who argued that the South couldn’t survive without slavery. 

Third, slavery has huge opportunity costs – all of the labor and money that gets spent in training the Unsullied or the sex-slaves of Yunkai or the gladiators of Meereen is money that can’t be spent on improving agricultural productivity or investing in new industries.