Technically the idea has some merit, but using a standard fridge would be impractical.
For little money you could convert a mini-fridge for the purpose, cutting a circular hole in the top for the Anova WI-FI device and routing the cooling coil in the fridge to the cooking reservoir for refrigeration.
You would have to make sure the fridge was off during cooking, but this could be done either through timer or WI-FI outlet controller.
Technically you could then, after the cooking time was up, turn the fridge back on to keep the food cool until needed.
Of course, it would be easier to use a small compressor unit, cooling coil, and a standard cooler. Several cooler mods for sous vide machines have been made.
Again, you would have to make sure that the compressor was off during cooking.