I've had SQLCop-type tests on my list of things I should get round to implementing, but have thus far only really implemented some 'test coverage' tests, which are pretty specific to our naming conventions here.
I do note that SQL Test is a preview product from Red Gate, so hopefully there will be more tests in the full release. From reading http://blogs.lessthandot.com/index.php/DataMgmt/DataDesign/sqlcop-integration-with-red-gate (and a couple of comments on the below forum link) it looks promising. EDIT: George's comment above confirms this.
You could consider logging the request at the forum that Red Gate link to from their website for feedback - http://sqltest.uservoice.com/forums/140716-sql-test-forum
If I do get some more generic tests written soon for my own purposes, I'll certainly share them.