Can I use Linux in a 2011 Macbook Pro with a defective discrete GPU?
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/