Not in the way you describe, at least not as a common built-in camera feature. Machine-vision systems can detect motion, but consumer cameras generally don’t wait for multiple subjects to become still and then fire automatically.

Some cameras offer related features:

• focus priority: the shutter won’t fire until focus is achieved, but that does not mean the subject is motionless
• motion detection features on some models: these may raise shutter speed when movement is detected, rather than waiting for stillness
• burst shooting: taking several frames quickly so you can pick the best moment afterward

For your situation, the practical approach is usually to freeze motion instead of trying to detect “stillness.” Use a faster shutter speed, and if needed add flash to help stop movement indoors. Shooting a short burst is often the best way to get one frame where everyone looks still.