It's not quite true that gas stoves are efficient enough to produce little CO. CO does result from incomplete natural gas combustion. 84 pounds per million standard cubic feet is the general emission factor used and that's the case for large industrial boilers as well as household appliances. You can look at your use level and see that the
That said, we also have an unvented gas stove in our house, although we did just buy a vent for it. The CO detector is in the same room and has never even been elevated, let alone gone off.
I just looked at our summer gas bill (so no heating) and we used 15 therms/month. That's 0.0015 mmcf, so it results in 0.126 lbs/month CO using 84 lbs CO/mmcf. That includes our water heater, which is in another location and is vented. Our CO detector in the kitchen has never gone up to 1 ppm.