Not to my knowledge. A possible approach seems to exist:

"To add a fire detector to your Ring alarm system, follow these steps :
Download the Ring app to your mobile device and log in to your account.
Open the app and go to the main dashboard.
Press "Configure a device" at the bottom of the screen.
Select "Fire detector" from the category of available devices.
Follow the instructions in the application to scan and configure your fire detector.
Make sure your fire detector is correctly installed and connected to your Ring Alarm network so that it detects flames effectively. "

However, the non-Ring branded sensor, must work with the Z-Wave protocol.

Everything is explained on the Ring page.