IIRC an old school synchronous fridge compressor is rated around 160W. An induction motor is more-less a constant speed motor so if you don't supply enough power it will slip/stall, so let's keep that in mind.
To make it work you would need an inverter, a pure sine one at that, and some kind of way to stabilize the energy you produce by pedaling with some kind of battery or capacitor bank.
Most good quality pure sine inverters are rated above 85% efficiency (i checked) so let's take 85% as our efficiency, assuming worst-case scenario given the unstable power production.
So the sine inverter would need 188W of power just to run the fridge.
Add the inefficiency of your generator setup and ask yourself can you really produce this amount of power by pedaling?
Also let's not forget that fridges don't run constantly, rather they run only when they need to, so if you connect to the compressor directly, your pedaling would directly affect the temperature inside the fridge.
You could also use some kind of energy storage solution (battery bank or whatever) to produce energy by pedaling now and let the fridge use it later, but then you would have to add the charge-discharge inefficiency on top.
Serious cyclists often measure the power they produce and you might be inclined to use these numbers for estimations but we have to keep in mind that cyclists have the benefit of airflow to cool them down and the ones that care about their performance tend to me more athletic.
Unlike the average Joe, who would be sweating their ass off while pedaling indoors just to keep their beer cold