Microsoft 365 features that help users manage their subscriptions, account settings, and billing information.
As your on-prem AD has no knowledge of cloud-only accounts, and as you need to manage synced groups on-prem, the answer is no. You have some options there, you can import the objects on-prem or even use the writeback features that come with Azure AD Premium, but the easiest way is to go with your second question. For which the answer is yes :)