Yes. On iOS there is a Pause button on the recording screen.
On Apple Watch a downward swipe will pause a recording. Be careful not to start the swipe near the top of the screen - edge based gestures are reserved for system actions (start the swipe about 1/3 of the way down the screen).
The Mac version does not support pause and resume but does have a mute function that can be activated by holding down the ‘M’ key during recording.