Do I need to line my chimney to install a fireplace insert?

I have a fireplace with a clay flue. Above the fireplace, below the damper is a heat exchanger to capture heat from the smoke and transfer it to the air blowing through the heat exchanger. The air flows into the heat exchanger from vents below the hearth and comes out above the fireplace after ping through the heat exchanger. The heat exchanger appears to be permanently installed, and a 6" liner will not p through the heat exchanger tubes. Would it be okay to terminate a new 6" liner at a filler plate below the heat exchanger and let the smoke continue up the chimney just like it always has? Would this be a code violation? Do I have any other options, or should I just be happy with the fireplace I have?