Yep, this is what I do, too, since my fridge is really tiny. I put the bird in the cooler filled with brine the night before I need to cook it. I figure the salt in the water will prevent bacteria from growing and you end up with a nice, juicy bird!
Edited to add: I don't use Alton's recipe. I just use 1 c. of kosher salt in my cooler and throw the frozen bird into it (still wrapped up since it's usually still pretty frozen).
So, have you ever died from food poisoning doing this
I copied Alton Brown's recipe to post here:
Good Eats Roast Turkey
Recipe courtesy Alton Brown, also featured in Food Network Magazine
Prep Time:15 minInactive Prep Time:7 hr 0 minCook Time:2 hr 30 min
Level:
Easy
Serves:
10 to 12 servings
Ingredients
1 (14 to 16 pound) frozen young turkey
For the brine:
1 cup kosher salt
1/2 cup light brown sugar
1 gallon vegetable stock
1 tablespoon black peppercorns
1 1/2 teaspoons allspice berries
1 1/2 teaspoons chopped candied ginger
1 gallon heavily iced water
For the aromatics:
1 red apple, sliced
1/2 onion, sliced
1 cinnamon stick
1 cup water
4 sprigs rosemary
6 leaves sage
Canola oil
Directions
Click here to see how it's done.
2 to 3 days before roasting:
Begin thawing the turkey in the refrigerator or in a cooler kept at 38 degrees F.
Combine the vegetable stock, salt, brown sugar, peppercorns, allspice berries, and candied ginger in a large stockpot over medium-high heat. Stir occasionally to dissolve solids and bring to a boil. Then remove the brine from the heat, cool to room temperature, and refrigerate.
Early on the day or the night before you'd like to eat:
Combine the brine, water and ice in the 5-gallon bucket. Place the thawed turkey (with innards removed) breast side down in brine. If necessary, weigh down the bird to ensure it is fully immersed, cover, and refrigerate or set in cool area for 8 to 16 hours, turning the bird once half way through brining.
Preheat the oven to 500 degrees F. Remove the bird from brine and rinse inside and out with cold water. Discard the brine.
Place the bird on roasting rack inside a half sheet pan and pat dry with paper towels.
Combine the apple, onion, cinnamon stick, and 1 cup of water in a microwave safe dish and microwave on high for 5 minutes. Add steeped aromatics to the turkey's cavity along with the rosemary and sage. Tuck the wings underneath the bird and coat the skin liberally with canola oil.
Roast the turkey on lowest level of the oven at 500 degrees F for 30 minutes. Insert a probe thermometer into thickest part of the breast and reduce the oven temperature to 350 degrees F. Set the thermometer alarm (if available) to 161 degrees F. A 14 to 16 pound bird should require a total of 2 to 2 1/2 hours of roasting. Let the turkey rest, loosely covered with foil or a large mixing bowl for 15 minutes before carving.
Controlled temperature vs uncontrolled. In an uncontrolled and warmer situation you can end up with a lot of bacteria and become very sick after eating the turkey. 
what is the difference between Kosher and Table? I guess there is always google... 
