So in short, the answer is no. The aiMixShader is an Arnold specific node and would not run in any program you sent it to unless Arnold was running there too.
In order for FBX to support a wild array of programs, they need to limit what nodes are accepted to only ones that can be easily converted in the end program. For this reason, you will find that the vast majority of Maya nodes will not export correctly with FBX.
The answer to how to do this workflow correctly is just building the materials in Unreal. This is not the only answer, but it is the best approach especially since Unreal is a real-time game engine and you want to use nodes and workflows that are fully compatible with it. Good luck!
