You need to run checkdb periodically. It is the only way you will detect corruption and the sooner you can detect it, the better.

If it's a burden on the primary server, then restore on a secondary server and run it there. If you don't have 4TB, consider purchasing Red Gate's Virtual Restore, and running it on a server that uses a virtual restore. You need to run checkdb.

Disclosure: I work for Red Gate.