Flash Workers - Can They Display Images/UI

Question

I've jumped through all the hurdles and slaved away at the keyboard to make Workers work in Flash Builder. Now I can create a worker, start it, terminate it--the whole nine yards. Awesome.

My question today is: Can I use them to draw to the screen? What sort of voodoo do I need to perform to make that happen?

My specific scenario is that I have a long-running operation on the main thread. While that's going on I would like to use a worker to draw a busy indicator over the application. When the long-running operation is done I intend to terminate the worker.