What you will be dealing with is called stratification. Given a reasonable volume of water the difference can be quite remarkable. A one metre height of water can stratify water from 20°C to 95°C as long as the water is not disturbed and heated gently, even if heated from the bottom
The simple solution is to regularly stir the water, say once every five minutes. This would be OK for items only requiring an hour in sous-vide, but for much longer this can get rather tedious
If you are targeting temperatures in the 40°C to 65°C range a small aquarium pump would suffice to stir the water. Arrange the intake tube nearly floating on top, and the output tube weighted on to the bottom. At a pinch an aquarium bubbler would help significantly too. Both these devices will cool the water somewhat, but a stove top heater should be able to keep up
Example: Using a small bubbler in a large, well-insulated chest (Rubbermaid cooler, Esky, chilly bin etc.) with around 10 l of water at 60°C, keeps the temperature within 1°C from top to bottom. Heat loss is around 1°C per 30 minutes. By adding about 0.5 l of 95°C water every 30 minutes it keeps the temperature constant over a few hours
To get precise temperature control within ±0.5°C which some sous-vide recipes recommend, you will need a PID controller. For general home use with temperature control or ±3°C you could get away with a stove top heater, with accurate power control and a thermometer control system. PID is not that hard, so you might as well add that to your controller too
As far as food safety is concerned there is no issue. A few days at fridge temps won't grow anything scary.
Food quality may be a concern. Vegetables want to be able to breathe. Some will handle being sealed worse than others. The problem is having the plastic in contact with the vegetables will hold condensation against them and promote spoiling. Luckily, the kind of firm veggies that can benefit from sous vide will also handle being sealed for a little bit.
Just don't hold them for more than a couple days and watch for mold.
Best Answer
Here is why it's stupid:
High acid recipes often call for processing in a water bath for a mere 10 minutes to seal the lids. Recipes that don't call for the water bath universally call for the product to be refrigerated.
Perhaps high acid foods could be vacuum sealed instead of bottled and pasteurized. It seems feasible but this is not the sort of thing you should experiment with. The failure conditions are catastrophic.