After my upgrade I recieve this error:

Site Component Manager successfully installed this component.  However the SQL Server Principal Name (SPN) could not be validated in Active Directory.

Possible cause: The MSSQL Service is running under a user account, instead of the computer account.  In this case, SQL does not publish its own SPN.
Solution: Manually publish the SQL Server SPN in Active Directory.

The component  will operate correctly.  However remote site systems requiring access to  SQL Server (i.e. management points) might not be able to access the SQL database.  Refer to your ConfigMgr Documentation or the Microsoft Knowledge Base for further information.

We have a single site with SQL running on it's own box.

Do I need to manually publish the SQL server SPN in AD or can I ignore this error in our current enviroment?

IMO, I would set the SPN, just so that you can manage the SQL remotely.

Is the SQL instance running as a user account, local system, or local service? If either of the later two, then the SPN will get registered automatically. Otherwise, yes you you properly register the SPN.