I have an early 15" 2011 Macbook Pro that is affected by the defective discrete GPU.
I know there are workarounds in OSX to force the use of the integrated Intel GPU, or disable the drivers for the discrete GPU. However these workarounds either make the computer too slow to use or are not reliable: although initially disabled discrete GPU may be activated when using some software and then the computer would stop working.
I have found these instructions for Arch Linux that look promising, because they mention a way to enable only the Intel GPU:
https://wiki.archlinux.org/index.php/MacBookPro8,1/8,2/8,3_(2011)
This is a similar question, that would achieve the same goal, but it is unanswered and does not mention running Linux:
Macbook Pro: How to disable discrete GPU permanently from EFI?
Best Answer
Yes, you can user Linux on a 2011 Macbook Pro that has a defective discrete GPU.
I just installed Ubuntu 14.04 on mine and it's working correctly. I followed these instructions:
http://ubuntuforums.org/showthread.php?t=2157775
Update:
In this MacRumours thread you can find a procedure to disable the discrete GPU by modifying the EFI variables:
https://forums.macrumors.com/threads/force-2011-macbook-pro-8-2-with-failed-amd-gpu-to-always-use-intel-integrated-gpu-efi-variable-fix.2037591/