Microsoft 365 and Teams: use my own domain for email notifications

You can add your domain and configure it for Exchange Online, without actually having to create any mailboxes for it. To make sure mail flow is handled correctly (as in sent to the on-premises server), you need to then set the domain as Internal relay: https://docs.microsoft.com/en-us/exchange/mail-flow-best-practices/manage-accepted-domains/manage-accepted-domains#configure-the-domain-type

But in general, if you want to take full advantage of all Teams features, you need to "integrate" it with Exchange: https://docs.microsoft.com/en-us/microsoftteams/exchange-teams-interact