Although the fat may add some flavor to the soup it also changes the mouthfeel. Instead of having a nice clear broth soup which is light and refreshing the fat in the soup with coat your mouth leaving a greasy feeling and taste. I cant be completely sure but if you were using the chicken thigh to just add flavor and not leave the meat in the soup you could use a chicken stock that your either make or buy from the store. As was stated above you could remove the fat from the soup. I would like to add another method to what Foodrules stated.
-Take a metal ladle and fill it with ice. Dip the ladle into your soup being care not to go deep enough to actually get any liquid in the ladle. They key here is that the cold ladle will solidify the fat and have it stick to it. You just remove the ladle wipe it clean with a paper towel and repeat until the fat layer is gone from your soup. Its very effective and easy.
Poaching is about cooking something gently, until just done. This is good for chicken breasts: white meat has very little fat and connective tissue, which makes it well-suited to this. It's at its most tender when it's not overcooked. Dark meat will be fine too. As with most other methods of cooking, it just needs to reach the appropriate temperature in the center.
Slow cooking, on the other hand, is about bringing something up to temperature and cooking it there for a long period of time. (There's no temperature to reach - it'll have been hot enough for a long while.) With meat, this is good for tougher cuts, as the long cooking helps break down connective tissue and soften it up. This is amazing for something like a pork shoulder, which can be cooked for hours and hours, until it's completely falling apart. You can probably get some fraction of that effect with dark meat. White meat will be iffy.
As for your favorite topic, salt absorption, longer cooking will get you more penetration into the meat, especially if it begins to fall apart. That won't happen easily with white meat, though, so it'll be a small effect - possibly you could cook it a while then pull it apart with a fork to help. It'll be a bit better for for dark meat.
Finally, since you've posted so many questions asking basically the same thing, my two cents: the best thing to do is probably just to roast chicken (don't overcook it!), shred it, and add some kind of sauce with a decent amount of salt. Cook it a little bit longer if you like, and there you are. You can only go so far with boiling/simmering/poaching/slow cooking, no matter how much you try to optimize it, and you've already gotten the main advice in other questions: possibly tenderize it, cook it in salty liquid, and perhaps help pull it apart once it's mostly cooked.
Best Answer
rfusca already gave very good suggestions for the literal question from the title. However, you can also address your problem the other way round.
First, cook the soup until your noodles are al dente (but will become just right while cooling at a normal speed). Take the big pot of soup off the heat.
Second, take a small pot, and fill it with just one portion of soup per eater. Put it on the heat, and cook until the noodles are done. (Alternatively, put the single portions into porcelain bowls and microwave until the noodles are ready - it spares you washing an additional pot, but I wouldn't nuke a good soup for no reason).
Third, eat your cooked soup portions and let the big pot of soup slowly cool on its own.
Fourth, freeze the soup from the big pot. Finis.
Note that from a food safety point of view, you are better off with flash cooling the soup. But what I outlined here is probably much simple and hassle-free. Plus, 2-3 liters of soup minus a portion or two should spend less than the magical 4 hours in the danger zone while cooling. If you are doing this with a very big pot of soup and feeding lots of people, you should probably prefer a rapid cooling.