A long time. I base this on taking apart a friends trimmer to put a carb kit in it that was laid up last last August. It was still damp inside with fuel.How long do you think it takes the fuel in a diaphragm carb to evaporate? The only difference between running it dry and letting it evaporate is what gets left behind.
But I have seen carbs that were dry inside after being stores wet.
Regardless the rubber parts would be coated with a slight film of oil even if the fuel evaporated fully.