Getting rid of Status Bar on 4.1
No, the bottom system bar (that's the one with the home, back, and recent buttons) can't be hidden on a stock device without rooting it and using a custom system image. The soft home button is very important because it gives you a way to get back to the home screen that can't be overridden by apps: this includes getting out of an unresponsive or broken app.

On 4.0 and above an app author can temporarily hide both bars, but touching the screen or pressing any hard key (including volume) will bring them back, so that doesn't prevent people leaving the app. (And quite right! It would be crazy for stock Android to let one app take over the whole system.)


  The SYSTEM_UI_FLAG_HIDE_NAVIGATION is a new flag that requests the navigation bar hide completely. Be aware that this works only for the navigation bar used by some handsets (it does not hide the system bar on tablets). The navigation bar returns to view as soon as the system receives user input. As such, this mode is useful primarily for video playback or other cases in which the whole screen is needed but user input is not required.
  
  http://developer.android.com/about/versions/android-4.0.html


It's worth noting that a full kiosk mode (not letting the user leave the app at all) has been announced for Android L, but the app has to be a device administrator to enter this mode.