Generally, Kernel Upgrade means upgrade of DB Dependent files and DB InDependent files in your kernel directory.
The DB Dependent files consist of DLLs in Windows and similar other library files for other OS as well. So, logic, common sense and SAP recommends that Database should be down when you are doing a manual* Kernal Upgrade.
Lets say, you have not shut the DB and some file from kernel directory is in use. You will just get an error - "File is in use".
Again, the recommendations here is stop the DB, so that the file is no longer in user, instead of figuring out which PID is using that file and then just killing that process.
So, bottom line - get downtime approval for SAP and DB for Kernel Upgrade.
But stopping of database is not mandatory. Just stop Instance & services.
If there is no database activity like online backup going on, you can as well stop database since there is no user activity.
- If you have Java, Using JSPM for Kernel Upgrade is Generally a good option