I suggest starting with this Cook's Illustrated brining article for more information on brining.
Much of what would be transferred into your turkey is liquid from the osmosis, but some salt, and sugar if you choose to use it, would be added as well.
If you purchase an "enhanced" turkey that has already been injected, you don't want to brine it. The injection has a similar effect. If you've made an enhanced turkey in the past, you've already eaten a bird with added sodium.
Harold McGee states that the turkey will gain 10% of its weight in a combination of water and sodium. Your brine comes out to about 3.9% salt, so your 12 lb turkey will gain ((12 lbs * .1) * .039) = .0486 lbs = 21 grams of salt from a 3.9% brine. Your average soda has 55 milligrams of salt per serving. The total amount of salt from your brine will be spread over the entire turkey, so divide that amount by the number of servings you expect that turkey to provide to get the number of additional milligrams of sodium per serving of turkey from brining.
If at the end of the day you don't want to brine, in that same article McGee also suggests a way to keep turkey moist without a brine.
EDIT: I did my math wrong above, and have corrected the formula and results.
Not all turkeys are the same, and personally, I would not risk letting an entire turkey go rancid in the refrigerator. There is so much you don't know about this turkey:
How was it butchered? In particular, how long was it sitting on the block and was it packed immediately afterward or left sitting out for a long time?
How quickly was it cooled down to "transporting" temperature after butchering?
Was it transported immediately, or was it stored for a while before transport, and if so, what were those storage conditions?
How specifically was it transported? What were the environmental conditions, aside from temperature? Was it exposed to air? Could it have picked up any other contaminants?
Just how cold was the refrigerator at Trader Joe's? Are you sure that it's consistently that cold?
What if the turkey was shifted around? For example, what if some other customer picked it up, tossed it in a shopping cart, then after an hour of shopping decided to put it back?
How did she transport it? I'm guessing in a non-temperature-controlled trunk? How long was it in that condition/environment before finally making it into the fridge?
Was the temperature in the fridge turned down as far as it can go long before putting the turkey in there? If not, how long might it have taken to get down to the desired temperature, especially with a massive slightly-warmed-up turkey in there?
How cold does her refrigerator get? Is it a new refrigerator? Are you both certain that it gets as cold as the rep at TJ's is assuming? Have you actually stuck a thermometer in there to measure the environmental temperature around where the turkey would be stored?
I'm not expecting you to answer any of these; my point is just that there are so many variables, so many things that can go wrong, and the quoted 10-day storage period (as well as the sell-by date) is for storage under ideal conditions.
I've seen turkeys go rancid in the fridge after just 2 days. I've seen others take longer, but still far less than 10 days to go rancid. It's an incredibly frustrating and completely avoidable experience. Just put it in the freezer! She just needs to make sure she gives it a couple of days to thaw in the fridge, due to the size of the bird. A half-frozen turkey on Thanksgiving day is almost as useless as a rancid one.
Best Answer
Having done this several times in the past - it is to make the oil flavoured. Like the comments have said that one onion doesn't seem to be enough, and frankly it isn't. I typically use 2, and remove the skins as well as score them allowing the juices to weep out a bit. Additionally, I know some people who toss a de-seeded bell pepper or two in as well, and it turns out well.