Any potential complications from ms sql backup db to disk = 'nul', disk = 'nul', ...?
So... you are getting alerted when a backup doesn't occur, and you want to suppress these alerts for certain databases, that you already know you don't need to back up?

If this is the case, it is very likely the alert system is reading the contents of msdb.dbo.backupset and other associated tables.

If you don't have the ability to exclude those in the alerts (and you can't just ignore them or make an email rule to delete them), then why don't you fake out the alert system by manually inserting those records yourself?

WARNING: THIS IS PROBABLY DEFINITELY A BAD IDEA, BUT FRANKLY NOT AS BAD AS RUNNING UNNECESSARY HOURS-LONG CPU AND IO-INTENSIVE BACKUPS THAT GO TO NUL AND ULTIMATELY DO THE EXACT SAME THING

So I'm not going to craft the INSERT statements for you (see my note above about this being a bad idea) but you'll probably need correctly-formed and properly associated records in some or all of the following tables:


msdb.dbo.backupfile
msdb.dbo.backupfilegroup
msdb.dbo.backupmediafamily
msdb.dbo.backupmediaset
msdb.dbo.backupset


I'd run a trace while running a backup to see what exactly it writes. 

Good luck, but fixing the alert system is by far the best idea.