AudioWorklet polyfill source code is available at github. It is loosely based on Houdini’s AnimationWorklet polyfill, repurposed for running AudioWorkletProcessor (and AudioWorkerGlobalScope) in a Web Worker, and AudioWorkerNode in main thread. Audio output is through main thread ScriptProcessorNode (SPN). Worker and SPN are interconnected via SharedArrayBuffer.
SharedArrayBuffer is very cool. Chrome stable seem to work with 256 sample buffer size without audio glitches in OSX 10.12.4. Firefox requires 512 or 1024 to be glitch-free, but that may be related to SPN deprecation, not its SAB implementation.