There is a current system that allows you to use email notifications. You can find this option in Game Settings.
Then you can keep your email open in another tab and a (1) will appear when you have a new mail.
Also, if you are using Firefox, you can install ConquerTell
which will bark a dog at you when a turn is ready.
If you are using MacOSX, there is a widget you can download which will do the same thing.
Since there are so many options already, I doubt this will be implemented.