I would like to know is it possible to induce RF emissions (incidental waves (re-radiation) from a RF device that is not transmitting ? The purpose of this testing is discover whether there is a hidden undocumented and undisclosed embedded RF transmission device that is likely in fact powered on but not transmitting and its transmission frequency range is unknown.
There is no foolproof way but indeed it is possible in some cases with non-transmitting devices. In fact that is how some "bug sweeping" devices called NLJD (Non-Linear Junction Detectors) work. The key is to sweep a frequency and look for faint return harmonics. Any non-linear device will clip the waveform and cause a "retransmission" As long as you have a way or getting some energy into the device then you should get a response back. The non-linear device may be protection diode on the IC pads, transistor on power supplies and even voltage regulators.
It is very hard to do in some cases as the signal can get swamped/absorbed by capacitance.
If you have a perfectly shielded device then it becomes increasingly difficult. But shielding a device that has openings for sound is also hard to do.
Looking for faint frequencies from on board clocks is also possible, but there is usually a very large ambient level of electronic noise in the environment.
Although it is possible to detect electronic circuits by the fact that they will generate low level harmonics of an incident RF signal (when powered or not), in this case you are asking to detect an RF circuit adjacent to a known 'benign' circuit. Typically the benign circuit will generate as much or more re-radiated harmonic energy so this approach won't be reliable.
The only real possibility is to perform a frequency scan, and detect any band-specific absorbtion of energy - this would indicate the presence of a resonant circuit (oscillator, filter, antenna), but it is perfectly possible to build a transmitting device without any particularly frequency-sensitive analogue parts. A DDS transmitter without a tuned antenna seems hard to detect.