Possibly, but she wouldn't start to sit until she had laid a complete clutch, because that's what all birds do. They lay one egg a day until the right number for their species is in the nest, then start incubation so all the chicks hatch on the same day. So by removing the eggs you will be giving her a break from sitting even if she goes on laying daily.
If you kept coturnix quails, or chickens for that matter, you would want them to lay an egg every day, wouldn't you, and would remove it to keep them laying? And if you wanted the maximum number of chicks, you would probably hatch in an incubator.
If you want her to sit another clutch, you might let her try once she's had a month off, maybe?