That would be covered under the terms of your policy. In general that is what supplemental, (secondary) insurance is primarily for.
Most "supplemental" plans pay the 20% that Medicare didn't pay only AFTER seeing an "explanation of benefits" statement--i.e. proof that Medicare paid their part. If Medicare denies a service all together, the supplemental plan is often under no obligation to pay at all, as they are there to "supplement" Medicare, not take the place of it in cases of denial. This is especailly true if Medicare denies because the service was deemed "not medically necessary".
So, in short, no. Medicare supplements often do not cover services if they are denied by the primary (Medicare).