Yes! Any user with Admin permissions can flip the proverbial kill switch to stop all recording and flip it back on anytime you'd like. You can also selectively turn recording on and off by domain.
Navigate to Settings > Recording and change the Recording for [Account Name] toggle. It is important to note that no data will be captured until you turn recording back on. Be sure to toggle it back on when you're ready to start recording again.
Note: When you turn off recording, sessions that were already underway may continue to record for up to one minute, so you may notice a few more sessions populate even after you’ve turned off recording.
What about Mobile recording?
If you use FullStory for Mobile Apps and you also want to disable or pause recording for mobile, make sure to turn off recording on the Mobile Recording Settings page as well.