Hi Andrew,
A good idea but almost certainly not usable.
Gas and smoke detectors work by having a sensor that is tuned to the chemical compound(s) targeted by the device.
The sensor takes a unique property of the target material and converts that property into an electrical signal that can then trigger an alarm.
For instance, hydrocarbon detectors (like the LIDL device) work by a flameless combustion of the gas on a small piece of platinum catalyst - and measure the voltage produced by the combustion; and a smoke detector works by smoke particles in the air blocking an electrical signal - as more smoke builds up the electrical signal reduces.
If the anaesthetic gas was, say Nitrous Oxide, then an exactly matched detection system is required - a dedicated combination of metals that converts the gas into something else - and then measure the voltage produced by the conversion.
You can buy such a sensor system, targeted at a particular gas - but choose the wrong sensor or if the crims use a different gas - then it'll be blind to the gas.
Robert