Q1
Is it necessary to do a database integrity check (DBCC check) on
mirrored databases?
Comment reply by Denis Rubashkin
Mirrored databases are in restoring state so you wouldn't be able to
run dbcc checkdb on them even if you wanted that.
Q2
Yes, right, but I mean principal database (which is mirrored) , not a
mirror one
Yes, you should.
A few of many more reasons as to why
What if a page that is rarely used gets corrupted?
When do you want to find that out?
Consider a scenario when a disk suddenly became unresponsive when SQL
Server was writing into it. This will obviously cause the data to
become corrupt; however, this corruption will be detected only when we
try to access the pages that had become corrupt; and this can be
months after the corruption was actually introduced. Similarly, a bit
flip while writing data to the disk subsystem, caused by a disk
driver, can cause corruption, and this might be actually detected at a
much later point in time.
Kernel Drivers and softwares like Antivirus, that have the ability to
take Kernel Level Handle on files, are also known to cause database
corruption issues. In case you have Antivirus Installed on the system,
please ensure that you exclude the SQL Server Database Files from
Antivirus scans.
Source
In short
You should always run integrity checks on your (principal) database(s). If the database is too big the next best thing is offloading the dbcc checkdb
to a restored backup. More on that here
Corruption can still occur due to hardware failure, an application such as antivirus getting access to the pages and causing corruption, ....
I am also not sure if there is any risk if mirroring does not repair
pages in some cases
Another reason why you should be doing integrity checks.
You could use ola hallengren's solution for running integrity checks.