DragonEgg is an LLVM backend for GCC: http://dragonegg.llvm.org/

There was some discussion of joining forces in the early days of LLVM (ca. 2005 I believe), but for various reasons that did not go forward. Licensing is indeed a big issue: GCC has had the explicit goal of making proprietary plugins technically infeasible, which leads to avoidance of some modularization/decoupling opportunities.

There has been recent talk of it. See here for a link and (brief) HN discussion: https://news.ycombinator.com/item?id=8149810

They already do- for a long time before Clang was ready for prime time, the default compiler on OS X was GCC with an LLVM back end. I'm not sure if any of this ever got merged into mainline GCC (the work was done on a pre-GPLv3 fork of GCC), but the code is widely available per the terms of the GPL.