Based on your edit to your question, and with some additional thought, I'm going to answer this differently.
Soured milk differs from what you called "spoiled" milk in only one way- what wild bacteria reproduced faster: bacteria with tasty waste products or bacteria with disgusting waste products. With that in mind the major potential problems with using this milk to make yogurt are:
- If the wild bacteria crowd out the yogurt culture
- If the yogurt culture is not able to work because the milk is too sour.
In making homemade yogurt neither of these should be a problem.
In making all yogurt- including yogurt made from raw milk in commercial settings- the milk is heated to 190F for some time to denature albumin proteins and to partially sterilize the milk so that the yogurt cultures will have the upper hand. This means that all yogurt has been pasteurized and the fact that the milk was purchased raw is a red herring. This will make problem #1 above unlikely. Not heating the milk will leave you with @rumtscho's answer- you can only guess what you might get by incubating it.
As for problem #2. Milk proteins begin to coagulate at a Ph of about 4.6. The target Ph for yogurt is usually 4.5. When making yogurt, Streptococcus thermophilus brings the milk down to about 5.0 and Lactobacillus Acidophilus takes over and brings it down to 4.5. Lactobacillus Acidophilus is active well below this Ph. Therefore, if your milk is not already thickened then it is, by definition, not too acidic for the yogurt culture to work.
Unfortunately, as the commenter from your first link indicated, heat combined with acid will cause the milk to prematurely denature. If you milk is too sour already then heating it to 190F may cause the protein to precipitate out and you would have paneer (sort of). I looked but was unable to find at what Ph milk proteins will denature at 190F.
http://www.foodsci.uoguelph.ca/dairyedu/yogurt.html
http://food.oregonstate.edu/learn/milk.html
If you can strictly verify the handling of your raw milk to have confidence that it has not been contaminated with harmful bacteria, and if the milk has only slightly soured so that it can be heated without breaking, you should be able to successfully make yogurt out of it knowing that the texture might vary from that of your starter.
Greek yogurt is simply strained yogurt. It was only fairly recently that Greek yogurt was widely available in the United States, so prior to wide availability, a simple substitute was to strain normal yogurt.
The type of sauce you are trying to make would definitely use a strained yogurt. Whether you wanted to strain your own or buy strained yogurt (aka Greek yogurt) is really up to you. In Greece, sheep's milk was traditionally used for yogurt, but now there's a lot more cow's milk too, so either would be authentic. I would think that full fat would be the most authentic, but not the healthiest, as I doubt low fat varieties were used traditionally (if they even existed).
The American use of the term Greek yogurt is really just one of branding. Many other areas in the middle east use the same style of strained yogurt. The Greeks also have plenty of normal (unstrained) yogurt.
Best Answer
The biggest reason to heat milk to almost boiling before fermenting is that it improves the texture of the yogurt.
During fermentation the bacteria consume lactose and produce lactic acid which causes the milk proteins to denature and coagulate trapping most of the fat. The proteins involved are primarily the casein proteins.
When this happens, there is still quite a bit of protein left that isn't bound up in the new casein mesh. All of the albumin proteins are water soluble and will not add to the structure of the yogurt.
These albumin proteins denature when they are heated. For this reason recipes universally call for the milk to be heated to 190 and then cooled. The albumin is denatured and is able to tangle up with the casein during fermentation and add to the yogurt structure.
Skipping this step will make a very profound difference to the structure of your yogurt. Without it your yogurt will be thinner and much more fragile. When you scoop it there will be more whey and all that albumin will wash out in it.
According to Harold McGee (On Food and Cooking pp 48)
"These treatments improve the consistency of the yogurt by denaturing the whey protein lactoglobulin, whose otherwise unreactive molecules then participate by clustering on the surfaces of the casein particles. With the helpful interference of the lactoglobulins, the casein particles can only bond to each other at a few spots, and so gather not in clusters but in a fine matrix of chains that is much better at retaining liquid in its small interstices."