Earlier smoke detectors use a collimated LED beam on one end and a Cadmium telluride photo-diode on the other end...any airborne particle that drifts between the two with sufficient density of obstruct light, changing the signal voltage of the photo-diode [or, if its a cadmium sulfide photo-resistor, then a sudden change in resistance] and trips the alarm...
Then there was a Gen II that was much less sensitive to airborne dust. The photo-diode is mounted perpendicular to the beam of the light. The theory of operation goes that when theres sufficient dust in the atmosphere light will scatter and some will hit the photo-diode and trips.
But now everything made in China, a cheaper but more technically-difficult-to-understand version came about using a small unit of a specific radioactive isotope [usually Americium-241, half life 432.2 years...aren't you glad they didn't use Americium-243 with a half life of 7370 years? :
] in an ionization chamber with two electrodes separated like a capacitor and a low current bias across the electrodes. incoming smoke or other airborne particles will absorb beta [or was it alpha? :-/] particles and break the ionization and therefore cuts off the current flow between the electrodes...creating an open circuit and will scream like a banshee until its removed.
Occasionally a quick spray of canned air can alleviate the squee...but other times the ball peen hammer comes out and...and never never trust the hush button will work when you need for it to work
Whether or not it will depends on a couple different things.
***Dimensions of your room***
+fog will quickly distribute itself on the floor...under the assumption what your using [glycerin] is denser than air and therefore clings to the ground, it will take some considerable time for it to reach the detector if theres room on the ground to faciliate its expansion
***Nearest source of airflow***
+While the fog is rolling around, if your HVAC utility is running [AC/heat/fan] the fog may circulate in the room and if your alarm is in the path of it...then yes
***Sensitivity of your alarm***
+assuming that its the ionizing version [if you see a black cylinder beside the battery tray it most likely is] the proximity of the electrode/plates and the current stability of the forward bias. the farther the plates the less sensitive it is.
Of 8 alarms one kidde brand was way too sensitive and would go off in the hall after I took a hot shower and opened the bathroom door...and its also the fastest battery drainer in the house. I finally got ticked off one day and took it outside, lay on ~10mg of powdered magnesium on it then...
But anyway, with sufficient fog within close proximity of the smoke alarm...it
will go off. As mentioned above...with our current smoke alarm technology we have not been able to create something that distinguishes between smoke and other pollutants :-?