As Android Police pointed out yesterday, soon 'round icons' will be supported in Android 7.1/Pixel Launcher. In fact, many of Google's apps are already shipping with round icon variants. I spent yesterday looking into this, and the end result is full support for round icons in Action Launcher.
You can use these round icons in three ways:
1). To use round icons only for apps that include such icons: Settings -> Display -> Prioritize round icons.
2). To replace all icons with a round icon pack: Settings -> Display -> Icon pack -> Pixel Launcher.
3). Pick the round icon variant when editing a shortcut via Quickedit (assuming the app has a round icon).
I'm in boat 3. I like the dedicated circular icons in say Hangouts and Maps. I'm far less of a fan of the "take an existing icon and put a white circle behind it" look of Gmail and Play Music.
Long time Action Launcher users will know I don't normally release new features in point releases, but this seemed cool enough to warrant an exception, so enjoy!
Grab Action Launcher from the Play Store: https://play.google.com/store/apps/details?id=com.actionlauncher.playstore
Note: this release is going to the beta group first. Join that here: https://play.google.com/apps/testing/com.actionlauncher.playstore
Screenshot gallery: http://imgur.com/a/yEVaz