It will work but if you are thinking about microvolt level signals the bias will have to be exceptionally stable and the temperature kept stable, the signal will be tiny compared to the voltage needed to provide partial bias. Also remember that class C is not linear, you will introduce distortion which in a small signal scenario will mean intermodulation and spurious carrier mixing problems which implies strong filtering before the input as FvM stated earlier.
I think I know what you are trying to achieve but I doubt you will get the results you want. I think you are trying to pull the stronger signal out of a noisy background by setting a threshold it has to exceed to be audible. A kind of squelch but at antenna level voltages. Consider that the filtering you would need to isolate the wanted signal probably does 99% of what you want.
Brian.