I found some interesting research papers about this.
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Hatching performance of Japanese quail from eggs stored for different periods - a preliminary study - this article says, that although quail egg quality deteriorates during prolonged storage, the researchers still had good results hatching quail eggs stored for 24 days, which is longer than hen eggs.
"Although chicks obtained from the oldest eggs (24–32 days) showed significantly lower activity, poorer down quality and limb malformations, this did not significantly affect the differences in their overall evaluation."
The optimal eggs for incubation were considered to be those weighing 11.51–12.50 g. Researchers observed egg weight loss during storage, due to water transpiration.
Eggs in this experiment were stored at "physical zero conditions", which is a temperature at which embryo is not developing.
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Egg Storage and the Embryo" - this article discusses optimal temperature for egg storage; 15°C is considered "physiological zero", but in other experiments eggs were stored at room temperature. Also, eggs stored for longer time may not start developing in the incubator right away, so the incubation time may be extended too.