Conversion Gain Definition for DSB-SC Upconversion
You have to define what you mean by 'conversion gain'. Once you've done that, the question resolves itself. 

Usually, when buying balanced mixers from a catalogue, the manufacturer specifies conversion gain as 'wanted sideband power' / 'input power', which results in a figure of -6dB for 'ideal' mixers. It's constant because in an RF mixer, the LO power is constant. But that's a physical system.

If you want to define derived terms from a mathematical formula, then the definition will yield whatever you put into it.