...I think its a higher concentration of CO2 relative to oxygen that kills you...so yes I think the CO2 detector is a good piece of equipment to add.
CO2 (carbon dioxide) isn't the issue, CO (carbon monoxide) can be a concern with incomplete combustion but most of these heaters run fairly efficient so before those come into play you run into the problem people over look which I mentioned and that is low O2 (oxygen). The unit is burning the oxygen out of the air, that's just how combustion works, and if its not replaced you go do sleep and don't wake up. Other than someone else showing up and noticing you becoming sleepy/disoriented most people have no idea they are in an oxygen deplete environment. If its hovering boarder line a headache may be your clue.
Be prudent and keep some ventilation going. A CO detector sure isn't going to hurt the situation but don't get a false sense of security from it.