I suggest you read the transcript to the Good Eats show on freezing, or, better yet, find a copy of the episode to watch. (Good Eats is an American TV show focusing on food science.) Here are some relevant excerpts:
[In the freezer,] any present bacteria are going to have a devil of a time finding the moisture they require to live, breed, survive. Since they themselves contain a considerable dose of H2O, freezing halts bacterial activity altogether, though some of the little beasties can survive to decompose another day. While it is in this frozen state, the meat will remain unspoiled for years. But there's a problem. You see, home freezers work very slowly. That means that as those little H2Os start to line up inside, they'll create huge, sharp, jagged crystals that will rise up, slicing and dicing their way through cell walls, muscle fibers, and pretty much anything else that gets in the way. Now while frozen, you won't notice this damage. But when it comes time to thaw, all of those perforated cells will start to leak out moisture all over the place. It's called drip loss and it's not a sign of good eats.
Therefore, if you are buying the meat fresh (i.e., it is not already frozen), then you need to take special care in how you freeze it:
One good way to prevent drip loss is to freeze the target food very, very quickly to a very, very low temperature. So that instead of creating huge, jagged, nasty ice crystals, you get very, very tiny little ice crystals.
The episode goes on to describe a process for freezing meats at home (basically, the idea is to use small pieces of meat, freeze them separately on a sheet tray, and then once they are frozen transfer them to a bag for long-term storage).
Even though the meat will technically be safe to eat for years, there are a few caveats. For one thing, the environment in the freezer is very dry. That can cause moisture on the surface of the meats to sublimate and form ice crystals, otherwise known as freezer burn. This can be avoided by packaging the meat in a vacuum (e.g., vacuum sealed bags), however, if you don't have a good vacuum sealer, I would suggest limiting their freezing to 6 or 8 months in order to avoid freezer burn. Another reason to make sure you use an air-tight container is that fats are very good at picking up flavors of other items you might have in the freezer.
I am fairly certain the "fats will surely go bad" claim is a myth, especially since fat alone is a good preservative. Perhaps you should ask that question on Skeptics.SE.
I'm not exactly sure why you're trying to brine then boil; you should be able to simply boil your chicken in salty stock and get plenty of salt into it. It won't take nearly as long as brining, because things happen faster in boiling water.
Assuming you boil for any significant length of time, much of the salt will indeed come out into the cooking liquid, and you'll end up with your soup approximately as salty as the chicken. (If the chicken is in large pieces, this of course only applies to the part the brining and cooking liquids can actually reach.)
Best Answer
I make stock from my leftover chicken bones and vegetable scraps. I just dump them in the pot still frozen, cover with cold water, and heat until it's a bare simmer. Simmer the stock for 2-3 hours or so, or until it tastes like soup instead of water. (But be careful not to boil, since the stock can get cloudy if you let it get up to a full 100C.) I have made this with both cooked meat and uncooked.
Uncooked chicken (whether frozen or not) will give you a mildly-flavored white chicken stock. If you brown the meat first, you'll get a stronger flavor and a brown chicken stock. (See here for a discussion.) If your chicken isn't cooked, you'll want to roast it to get all the nice brown bits from the Maillard reaction, which will defrost the chicken in the process.