I have this model MBP, and yes, it failed exactly as described. I think the problem is made worse when paired with the thunderbolt screen, which forces the dedicated GPU to be used instead of the Intel GPU. It runs super HOT all the time, even when simply web browsing. Many have found a utility called smcFanControl to force the fan to run at full speed at all times in an attempt to compensate for a bad design.
There are numerous YouTube video's of how to "cook" the logic board in an oven for 3 min @ 375 deg to reflow the solder and I found this does fix it temporarily, so its definitely a solder ball issue. Ultimately, I found a repair service on e-bay that for $150, replaces the solder balls on the BGA with lead balls (supposedly) and this is a more permanent fix. According to him (and he seems legit) the lead-free BGA balls suck, and over time fail with extended heat / use.
I hope there is a class action on this one, because I paid almost $3k for this laptop and it only lasted 2 years!