Recently I've been seeing an increasing number of packages with labels such as "Contains no added nitrates or nitrites (except those naturally occurring in the celery juice powder)". Does celery powder have any use other than as a method of sneaking nitrates into things?
Does celery powder have any non-preservative use
food-preservation
Related Solutions
Does the quality degrade? Yes, yes, a thousand times yes. Garlic (like onions and other members of the allium family) begins to undergo chemical changes the moment you cut into it. It's the same phenomenon that causes you to tear up when you cut into an onion.
Quoting liberally from Wikipedia's article here...
The phytochemicals responsible for the sharp flavor of garlic are produced when the plant's cells are damaged [...] The resultant compounds are responsible for the sharp or hot taste and strong smell of garlic. Some of the compounds are unstable and continue to react over time.
Ever notice how garlic becomes sweeter and far less pungent with even a brief sautee? That's due to the instability of these flavorful compounds and how they break down when cooked.
A large number of sulfur compounds contribute to the smell and taste of garlic. Allicin has been found to be the compound most responsible for the "hot" sensation of raw garlic [...] The process of cooking garlic removes allicin, thus mellowing its spiciness.
If you're defining "quality" as how well the preserved product maintains the same characteristics and flavors as the fresh version, this is already quite degraded. It may still have its uses but don't expect this to be even remotely substitutable for fresh garlic.
Is it safe to eat after a full week? Possibly, but very difficult to verify at home. @rumtscho's comment nails it: if this was sufficiently dehydrated, it might be okay (in which case it will be even further from fresh garlic in terms of flavor and usage) but that is unlikely, and this should be treated like any other cooked food.
If you want to maximize the shelf life of your garlic, just keep it whole! Unpeeled garlic will keep for weeks if kept cool and dry, and you can break off individual cloves as you need them. All that it takes to ready one for cooking is a heavy pot to smash the clove with and a quick pass with a knife.
With just those four ingredients (plus maybe some seasonings), your hot sauce will be a "low-acid food" which means that to be shelf-stable, it needs to be canned at 240F/115C. This means that you will need to use pressure canning to seal it (pictoral guide). If properly pressure canned, it should be shelf-stable for months to years.
This has two drawbacks for you: first, it requires getting a pressure canner (or using a pressure cooker and really small batches). Second, it does mean that you're going to be cooking the hot sauce at 240F, which may lead to it being more "cooked" than you necessarily want it to be. If you have a pressure cooker around, I suggest trying that with one jar and seeing how it tastes.
Best Answer
Yes, it tastes of celery. Celery is one of the three ingredients of mirepoix, the vegetable mix which is ubiquitous in French cuisine and has spread to many others. Current large-scale food production rarely includes slicing fresh vegetables into small cubes and browning them in a pan, but they try to add the ingredients in more convenient form. So, if you eat powdered soup or similar, it can be used for that.
On the other hand, if you are eating cured meat, then the most probable reason are indeed the nitrates. If you are looking at a certain type of cured meat (e.g. bacon), it is impossible to produce the same cured meat without nitrates *, but there are customers who are scared of "chemicals" and are more likely to buy the food if the label states that the nitrates are coming from a plant source.
* And in general, most types of curing are done with nitrates. There are types done without nitrates, e.g. the prosciutto pointed out in the comments, but they are the minority. And it is more difficult to create a safe process which cures without nitrates, since they have a preservative role.