Current mode switching has side effects that make it useful for many ham radio circuits.
For regenerative radio circuits the Tanh response curve gives smooth regeneration control.
The multiplier effect allows for mixer circuits and AM moduation circuits.
Well if you say 1 mA into the base emitter results in the base emitter junction having a resistance of 26 ohm, the 1uA gives a resistance of 26k and 1 nA 26meg. The input resistance of Q4 is then about 8 meg. Q3 is a short at RF so the tuned circuit sees a load of 8 meg in parallel with 4.7 meg.
Q3 only provides an exact current related voltage drop for biasing, and even without the bypassing capacitor has such a low resistance it can be ignored.
There is no point in using a collector load resistor for Q4, that would only throw away gain.
The sensitivity of any AM detector falls off with increased frequency. I have no measurements to say how well the circuit will operate at 20 Mhz, probably it will be fine.
Obviously with 3 nA going into the base of Q4 each electron counts and natural fluctuations in the exact number of electrons flowing at any particular time cause Gaussinan noise. You can hear some noise when you connect an audio amplifer. I would say the level is low enough not to be any problem, but loud enough to provide reassurance that the circuit is working.