For example, if you used eggs or milk that was not yet spoiled but right on the verge… does using it as an ingredient in a cooked/baked product give you additional time to consume the product before it goes bad?
Don’t need answer fast 
Generally yes if something is cooked sufficiently to kill off dangerous bacteria. However, it is not usually doing anything like resetting the shelf life, instead the food is being substantially changed and has a new shelf life based on it’s composition and content.
And then if you cook some things enough they’re shelf life extends to forever. Charcoal doesn’t go bad.
Even if you kill bacteria, it doesn’t necessarily get rid of toxic byproducts from the bacteria. For example, botulinum toxin can survive cooking, depending on how hot it gets.
Milk and cream tend to go bad within a month or so in the fridge, but once I make ice cream, that ice cream as far as I’m concerned is edible forever when kept in the freezer. Not that it lasts all that long.
Meat too. Raw chicken gets rather unpleasant in the fridge after several days. Cooked chicken lasts far longer.
In this context, the question was "is at home cooking able to replicate the shelf life of a commercial product ? ". NO , NOT AT ALL, NO WAY.
In most cooking, water, oils, is added. So the cake mix has a long shelf life, but once cooked, the cake only has a few days of life.
Note that killing the bacteria might not destroy the poisons ; also there may be an amount of enzymes left, and the enzymes encourage bacteria by providing the correct food substances for bacteria… Now if the food is then left to grow bacteria again, perhaps in the warm conditions of a picnic basket, then the bacteria grows faster , and more poisons are made (Not due to the poisons/irritants/immune system triggers already there, but the two lots of poisons add together… to result in food poisoning … )
Also, in some products there are preservatives to give a reasonable shelf life, but it must be assumed that the preservatives are LOST during cooking.
Even charcoal has its limits, especially if you’re storing it in an outside container in humid Seattle winters. I didn’t eat any, but I’m assuming fuzzy blue charcoal is bad for you. 
No. the maximum you can leave chicken and other meat in the FRIDGE is a few days.
The freezer is different, of course, because the bacteria, fungi, mold, etc is not able to grow. However the product spoilage may be due to ice crystal growth and freeze drying and loss of flavours and preservatives… But generally after freezing for months, you could if you like keep the product in the fridge for A FEW DAYS. ( Anything out of the freezer… consider it a sort of cooking.). Cooking it doesn’t vary that, it can be kept a few days, whether you cooking it straight away, or cooking it at the end of the few days, its a few days TOTAL
Shelf life means all sorts of different things. It isn’t just that something becomes unsafe the eat due to microbial action. Many cooking ingredients have a shelf life limited by ongoing chemical reactions that eventually alter the flavour of other important characteristics. (The process of staling for bread for instance is a change in the morphology of the starch grains that proceeds without any other agent. Flour oxidises over time, as do lipids.) Live foods (ie vegetables) have a life limited by the remaining activity in the plant cells. Meat continues to degrade as residual processes in the cells continue. Some foodstuffs unavoidably include some contaminating bacteria or fungi, and you need to use them before any of them reproduce to an extent that makes the food dangerous or unpalatable.
As noted by TriPolar, cooking usually substantially changes the nature of the ingredients. Your new shelf life depends upon the nature of what you created. Spoiled food won’t unspoil, and ingredients with a degraded state won’t undo their degradation (for the most part) when cooked. You might be able to argue that (say) a cake made with old butter that is partially oxidised will have a shorter shelf life because ongoing oxidisation will mean the off flavour will become noticeable earlier. However the cake will still probably have a shelf life limited by other factors anyway.
(bolding mine)
WAY, WAY AT ALL. I answered the question asked, and then you apparently stopped reading my post after you misinterpreted it.