There's a chance, but I personally would not risk it since CO poisoning can and will cause permanent organ damage if you fail due to the effects of hypoxia on the major organs as well as the effects of CO on mitochondria. So, I would buy a proper CO detector that goes up to 10K PPM.
That being said, if I absolutely did not want to test, I would use a considerable amount more charcoal than I needed as well as multiple grills/buckets, chimney starters, etc.
I will also note that you cannot just "get some coal and light inside your car." There are a number of steps you need to take such as sealing it up, ensuring that it will not catch fire, and getting in only once the atmosphere inside the vehicle is >1% CO, as otherwise the method will not be peaceful. This is a common misconception - essentially, CO is not an inert gas like nitrogen so you need a sufficiently high concentration to pass out and not feel the effects of it alongside the smoke (and no, I would not advise knocking yourself out before >1% is achieved, because something may happen while you are asleep that reduces the CO output and thus just ends up giving you severe organ damage but not killing you). This is another reason why it makes sense to test. You need to ensure that there will still be enough CO even if you open the door and then get in or whatever kind of setup you rig. Another consideration is how low to the vehicle's floor you would be, as the PPM is going to higher if you're not on the cabin floor, as CO is slightly lighter than air.
I would probably use a tent with a double flap and unzip one, then rezip, then unzip another and leave it unzipped. And I would conduct multiple tests prior to using such a protocol. And when I did it, I would leave the detector in the tent (at the same level/height that I would be at) prior to entering it for the final time so that I would know for certain that it was >10K PPM.
