On the desktop, yes. Why? Because all the innovation in organizing, displaying, and managing email was focuses on webmail. Not because it was a better platform, but because it was incredibly easy to deploy and cheaper to develop.
Where is the email client back? On the phone. People want access to their email if they don't have an internet connection. Used to be the same on the desktop when being online meant you were tying up a phone line at a per minute cost. Your desktop is always online now, so it's not an issue.
But I still believe we will see a return to native email clients because of the integration possible with other client software and services. We already see it on tablets and phones.