Water which enters Lake Superior remains there on average for almost 200 years, and then the water spends another prolonged stay in the other Great Lakes; perhaps another century or so total.
What this means is that should the area turn into desert, there would be a period of time during which the Great Lakes would survive as a kind of gigantic oasis. It would last for a time scale which would be historically important, on the order of a few centuries to maybe a couple millennia; I'd need to look at the geography closer to be more precise: the deeper the channels linking the Great Lakes to the ocean, the further they'd drain before getting cut off and the water loss being brought down to evaporation only.
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What this means is that should the area turn into desert, there would be a period of time during which the Great Lakes would survive as a kind of gigantic oasis. It would last for a time scale which would be historically important, on the order of a few centuries to maybe a couple millennia; I'd need to look at the geography closer to be more precise: the deeper the channels linking the Great Lakes to the ocean, the further they'd drain before getting cut off and the water loss being brought down to evaporation only.