There have already been a lot of experiments in putting React in a web worker (one example http://web-perf.github.io/react-worker-dom/), and unfortunately those experiments have had mixed results. Some things get faster, others slower. Some overhead to development and deployment. Etc.
Web workers incur some cost in moving data in and out of them, which is part of what complicates things. You can read more in the section on Workers in https://github.com/reactjs/react-future