when the game is paused you are not really meant to look around and interact with it much outside of a pause menu hence the entire game being paused. If you look at games in general, when you pause you can’t carry on interacting with it. The pause system is meant if you actually need to stop playing for a certain amount of time or to change settings, save, load, all that kinda stuff. When you pause the game state it pauses all the rendering and all that. There isn’t really a way around it unless you are willing to setup some kind of custom pause state in C++ which will pause the game but continue rendering objects onto the screen.
I use the Oculus Rift at work with the Touch and when the game is paused we actually advise the user to take off the headset as you’re not meant to keep interacting with the environment.
One work around is before you pause it, everything gets rendered. Only problem is you will get a massive performance hit and I doubt you could maintain the 90FPS required to use the headset.