If you just cut the jug portion of the silencer off, you get the airflow improvement along with cool air. You can keep the underhood funnel portion in place too for a stock look.
I think this will net more air than removing it since the plastic piping stretches the gasket in the entrance of the airbox. Without the silencer tubing in place, the gasket/seal expands a bit, reducing the inlet size.
You end up with something of a 'Y'.
Hope this helps,