Yes, but please note that it has to be turned on using the Bang & Olufsen app. To turn the power saving function on and off, add Beoplay H9 3rd Gen to the app and simply toggle "Enable automatic standby" from the product page as shown below.
When the feature is turned on, if Beoplay H9 3rd Gen are not paired or out of Bluetooth range for 15 minutes or more, they will automatically switch off to conserve power. However, if you want to switch them off while they are still within Bluetooth range, you can move the switch to the OFF position.
The Bang & Olufsen app is available for download here