Macbook Pro (late 2011 15") is stuck in a boot loop
Does this mean it has a dead GPU?

Yes. Absolutely. This means it is one of thousands GPUs killed by inadequate thermal design that finally bit the bullet. As all MBPs from that era are defective by design it is impossible to keep them around for the amount of time you would expect from a quality product.
If this machine is still around then it can be partially resurrected with a procedure like this:
https://apple.stackexchange.com/a/295805/251859
This bypasses the AMD GPU through a forced EFI variable. No amount of SMC reset voodoo or the like will restore a GPU dead MBP.
You might want to bake the chip for a flaky temporary fix like with the iBake procedure.
The only real fix though is to either sue Apple like they deserve for lying on this to us all or to replace only the AMD chip in question. That is way cheaper than to go the now defunct Apple road of replacing a faulty board with another faulty board.
Converting it over into a Linux machine makes the GPU bypass on a defective machine easier, but will not do much good for keeping it around long enough.