Canning for couple of days to one week of low acidic cooked food without pressure canning?
NO! Using your method you have created the perfect environment to grow Clostridium botulinum, so within a couple of days you very well could have a thriving colony of botulism rich food. 

From USDA Complete Guide to Home Canning


  Ensuring safe canned foods
  
  Growth of the bacterium Clostridium botulinum in canned food may cause botulism—a deadly
  form of food poisoning. These bacteria exist either as spores or as vegetative cells. The spores,
  which are comparable to plant seeds, can survive harmlessly in soil and water for many years.
  When ideal conditions exist for growth, the spores produce vegetative cells which multiply
  rapidly and may produce a deadly toxin within 3 to 4 days of growth in an environment
  consisting of:
  
  • a moist, low-acid food
  
  • a temperature between 40° and 120°F
  
  •  less than 2 percent oxygen.
  
  Botulinum spores are on most fresh food surfaces. Because they grow only in the absence of air,
  they are harmless on fresh foods.
  
  Most bacteria, yeasts, and molds are difficult to remove from food surfaces. Washing fresh food
  reduces their numbers only slightly. Peeling root crops, underground stem crops, and tomatoes
  reduces their numbers greatly. Blanching also helps, but the vital controls are the method of
  canning and making sure the recommended research-based process times, found in these
  guides, are used. 
  
  The processing times in these guides ensure destruction of the largest expected number of heatresistant microorganisms in home-canned foods. Properly sterilized canned food will be free of
  spoilage if lids seal and jars are stored below 95°F. Storing jars at 50° to 70°F
  enhances retention of quality.