No - running DBCC CHECKDB on any copy of the database that is maintained by SAN replication, log shipping, mirroring, etc is not good enough. That tells you nothing about the I/O subsystem on the main system. Only doing a full backup+copy+restore is a substitute for DBCC CHECKDB on the main server.
Cheers
Paul Randal
CEO, SQLskills.com: Check out SQLskills online training!
Blog:www.SQLskills.com/blogs/paul Twitter: @PaulRandal
SQL MVP, Microsoft RD, Contributing Editor of TechNet Magazine
Author of DBCC CHECKDB/repair (and other Storage Engine) code of SQL Server 2005