You can do that with Flash Professional. First you must create a loader that loads in and shows that SWF exported from InDesign. Then you add a full screen command to that loader (it´s couple of lines of action script code)
Finally you publish your project as projector.
For security reasons you can't automatically invoke full screen mode. There has to be some kind of user interaction—like clicking a button that puts the SWF into full screen mode.
I think Flash Projectors (exe and app) are operating inside their own security sandbox and therefore it´s possible to make full screen as an initial state. Same goes with Adobe AIR...
But if you run your SWF inside the browser, yes, user has to accept full screen state...
Right, I was assuming a browser.