Depends on the sensitivity of the device. It might be possible to pickup the EMF of the camera, even if it's not actively broadcasting.
Every current carrying trace is an antenna.
That would only be practically useful in an environment devoid of all other electronics. How would one tell between the non-transmitting spy cam and normal household electronics
By having some spatial/angular resolution. You'd need a large directional antenna or multiple antennas to have something similar to a phased array radar, but passively (i.e. listening only).
What you really need is a Non-Linear Junction Detector. These can detect an unshielded device with transistors, even if it's off.