If you absolutely want to go ahead with the terrible idea of putting an 820-3330 board into a machine that originally had an 820-2915, yes, it will fit. You will just need a lot of tape to hold the LVDS cable into the LCD connector on the motherboard, the latch is different on 2012 models and will not fit 2011 boards. So tape is necessary. Otherwise, everything else fits - battery, keyboard, trackpad, hard drive cable, webcam cable, wifi cable, battery indicator, speaker, are all the same.
This is a really crappy solution considering you will be paying $650 for a jerry rigged setup that is two processor generations behind. I would call this a complete waste of money. Let's move on to a real solution.
Step 1 is to get Apple to fix this $@$* for free. https://www.apple.com/support/macbookpro...
Step 2 is to get it back and run GPUtest on it until it dies again. Furmark with max settings. http://www.geeks3d.com/gputest/
Rinse & repeat until they're tired of seeing you, and then say you want something that works. Gosh, you're willing to PAY, but you just need something that will work. Be nice about it so they feel bad for you. They'll cave and give you a Retina with iris graphics - if you complain hardcore, you'll get one with NVIDIA discrete. Iris still kicks the $@$* out of that AMD chip so you'll be good, many find it's not worth it to ##&&% to get the NVIDIA - lots of escalating and time wasted for minimal return on investment.
Some will say this is unethical. I say it's unethical to sell a $2700 machine that dies for no reason and then to ignore your customers. When you see how easy it is to kill the one they give you back with Furmark you'll feel the same way - this is a really BAD laptop and they put billions in the bank selling this aluminum cat bed heater to the American public for $2000+.
This repair program only lasts until January 2016, and you bet your @%^ it will fail days outside that program. So do what you have to to get Apple to give you a proper machine that doesn't die watching YouTube videos before you're SOL.
Or you could spend $650 to put a used ivy bridge board from eBay with no warranty, that's slower than the retina in your machine... your choice.