How do I make Evolution check and also alert new e-mails, without maintaining major UI open?
As much as I recognize this is not feasible presently. There is currently a bug record at launch pad : https://bugs.launchpad.net/ubuntu/+source/evolution-indicator/+bug/508608
You can attempt mounting 'mail - notification - evolution', its intended to give assistance for Mail Notification. I had some troubles utilizing it, yet some individuals have actually had much better good luck than me.
sudo apt-get install mail-notification-evolution