I have the basic ideas that libGDX uses RobotVM to compile Java into llvm-like bytecodes and then platform-specified codes.
I was wondering if I could use AndroidJSCore in libGDX applications. It's for android, I suppose this should compile. The problem is it relies on JavaScriptCore, which was built in C/C++. Does RobotVM compile C/C++ codes?
It sound like you have a wrong idea of what RoboVM is (was) RoboVM was used by LibGDX to run on iOS. RoboVM was discontinued as of april 15 2016. LibGDX now uses Intel Multi-OS Engine to run on iOS.
LibGDX on Android uses Dalvik just like normal android apps. So if AndroidJSCore works with normal Android apps it should work with LibGDX too. But, you might be the first person to try it.