As far as I know it should work as expected. They have their own forum here: https://community.yatse.tv/. People on the forum say they're running OSs without Google Play, and instead they have microG.
Their dev says the account must be listed in Settings > Passwords & accounts.
Other than that, who knows? Pretty sure GrapheneOS hasn't made any changes to that part of AOSP, so if it works on other phones it will most likely work on GrapheneOS. It seems like they're helpful when users run into issues, so if you pay for the app I think they'll help you out via email or on their forum.