We understand what you are trying to do. There are two issues, the first is the signal itself biasing the UN-powered stage, particularly in TX mode. It wouldn't work properly but if it had a gain of 1 or more it would oscillate. The second issue is simply the parasitic capacitances and inductances in the loop around the powered part. The phase shifting through theUN-powered part could still form an undesired feedback path.
This is why I suggested applying a reversed supply voltage although as FvM pointed out, it has to be lower than the transistor breakdown voltage. The reversed supply will help to prevent the self biasing problem and at the same time might 'varicap style' reduce some capacitance in the remaining feedback path.
Commercially, the method used is to make two amplifiers but use diodes to steer the signal through the appropriate path. The idea is that signal passing through a forward biased diode sees a relatively low series resistance but in a reversed biased path it sees only the residual junction capacitance. By suitably wiring diodes, typically three in each path, you can present two low resistances in series with a small capacitance between them to ground -or- two small capacitances in series with a low resistance between them to ground. It makes a very effective and simple signal switch.
Brian.