A Joule thief is a specific inductive boost-converter topology, typically using a coupled inductor. Battery imposes the same space/weight costs. That seems unnecessarily complicated for this application. But I'll steelman your argument as "some means of surreptitiously storing energy."

You can design a two-channel current detector. One channel measures near-instantaneous current; the other integrates excess current over a defined window to detect cumulative energy consumption.

A capacitor can conceal transmission peaks, but it can't conceal the energy needed to recharge it. The relevant question is whether that additional consumption falls within the device's normal power variability and the detector's sensitivity. Given control of the electronic design you could intentionally lower the power consumption of the legitimate assembly to make such detection even easier.