If the static port get blocked, and no alternate static air source is fitted, will the transponder keep provide mode C?
It will stop reporting correctly as it is connected to the same static air line as the altimeter


  The transponder depends on an external altitude encoder to provide the digitized pressure altitude that the transponder needs for its Mode C replies. The encoder is connected the same static air line as the altimeter and is wired electrically to the transponder


However the transponder may not know the port is blocked and will still report the erroneous information it is receiving. If the port is blocked it’s pertinent to shut off altitude reporting manually.