I'm busy figuring some of this out, hopefully I can leave some advice to anyone else trying to use Wwise on Linux using Unity. Following an email with the support team, this is not actually supported, some don't hold your breath on getting full features working without some work. I am at least at the stage where I can make builds on Linux which can play audio using the Wwise SDK - though I'm still figuring out how to get audio working in the Editor.
Following the discussion of Linux users of another game (Polyball) - it occurred to me that there was still some linking issue with libSDL even though I installed it. Not sure if its a wrong version or perhaps a 32 bit vs 64 bit issue. Here's the thread
https://steamcommunity.com/app/368180/discussions/0/133259227521120753/?ctp=2
My solution to get audio working on Linux and get around the error "AkInitializer.cs Awake() was not executed yet" was simply to link to the libSDL that is provided along with steam (even though I'm not using steam currently). My library was located here ~/.steam/steam/ubuntu12_64/libSDL2-2.0.so.0
You can load it using LD_PRELOAD when launching your game, or you can simply copy it into the [GAME_NAME]_Data/Plugins directory.
However, to even get it building on linux, you need to fix a few issues including the one you mentioned. Throughout all those Linux classes you are looking at in Deployment/API/Generated/Linux, you need to change the existing #if statements to:
#if (UNITY_STANDALONE_LINUX && ! UNITY_EDITOR) || UNITY_EDITOR_LINUX
Furthermore, I had to Deployment/API/Handwritten/Common/WAAPI and disable those classes on Linux using:
#if UNITY_EDITOR && !UNITY_EDITOR_LINUX
Besides that, there was an errorMessage variable in AkWwisePicker that needed to be initialized on Linux.
After that, you can hopefully build on Linux and have a playable that has audio. Still figuring out how to get audio working in the editor.