Let's hope not. The healthy competition between the two projects has been a huge boon for the OSS community.
It will not be, because LLVM does not align with the goals of the FSF and GNU projects. A free compiler under a free license is a pretty central project for them. (Besides that, making predictions 10 years out into the future of software seems meaningless. Saying "this thing might still be around in like 2 decades, or not" is... not particularly noteworthy, nor damning)
Plus, I simply see no reason to believe this, even aside from that. If anything, GCC development has gotten far more active and improved greatly in the past few years, with consistently high quality releases, each bringing in major features, and adopting work from Clang, and bringing in their own unique work. It would seem each of these projects has livened up quite a lot over time and are offering higher quality than they ever have before.
What reason do you have to believe it will be completely abandoned? Just because there's an alternative available? That never happened with Linux, either...
I don't think the performance difference between them is significant, but Clang is much nicer if you want to use it as a library, add a new backend, etc. Basically if you want to do anything other than run it from the command line.
Oh also, Clang does cross-compilation in a not totally insane way.
I wouldn't be surprised if GCC is abandoned eventually, but it will be at least 10 years.