Can I disconnect a Corian Sink Overflow tube?
It's quite possible that there is hair or other gunk in the sink tailpiece or caught in the stopper.  It absorbs some of the sewage and then gets really nasty.  The stink could then freely travel out.  Try taking out the stopper and cleaning any gunk you might find.

This would solve the stink problem.

To answer the question about the overflow being sealed... it would violate plumbing code almost surely.