SQL Server Replication - Can destination db have stored procedures that source db lacks?
Yes, absolutely.

You would typically use transactional replication to move data between the publisher and subscriber(s) (although you can include other objects as well). Your subscriber (destination) database is fully writeable, and you can create stored procedures there, add indexes to replicated tables, and even create entirely new tables.

Be aware, you can also delete data from the replicated tables on the subscriber, which could lead to replication breaking and you having to re-snapshot.