Additional SQL Server features and topics not covered by specific categories
No, it does not get replicated and this is because it (the database/s) are on a separate instance on a totally different storage system. You have to run it on the Secondary on the databases there. If the database is mirrored, you won't be able to connect to it to run it because it will be inaccessible. So, some people take snapshots and restore it, and then run it on the restored snapshot. Then, there are opinions that you only need to run dbcc checkdb on the Primary databases and that suffices. We have checkdb set up to run on the Primary and Secondary servers. That way, if the database(s) are failed over to the Secondary, you are sure to get dbcc checkdb run against the active database. I hope this helps.