Yes on iPad
You can pause an experience using the Pause button in the upper left corner of the screen.
This will suspend any video and timing until you press the resume button. Any timing of your experience will also be paused while you are on the Paused screen.
Note: The Pause button is not available in Research mode as the timing of experiences is an integral part of the research data and so no interruptions are allowed.
No in VR
Currently the VR client does not allow for pausing. Opening the menu during an experience does not pause the timing or the video. You can return to the experience from the in game menu by pressing the resume button or pressing the menu button on your controller again.