As long as it's properly decoupled, power counts as ground, as far as RF and microwave signals are concerned.
With CPW, it needs a bit more thought to 'properly decouple' it for RF. In classic CPW, where you'd bridge the two grounds with a link to keep the grounds balanced, you'd bridge with a small ceramic capacitor. Note that the normally many μF power decoupling capacitors will not do this job, but of course you still need them in their normal positions to decouple the power for you.
Where you've annotated the 0.2mm gap at the top of your picture, you'd put a 100pF or so (depending on signal frequency, bigger for lower frequencies, at 12GHz 10pF is about 1 ohm, you'll have more series impedance from the physical length of the cap than its capacitance) across this gap. You'd need another one in a similar position at the signal destination.
These caps to ground will still allow a small amount of signal to excite the power track with respect to the ground plane. If the length of power line between these two caps is an unfortunate length, and resonates with your signal or harmonics in it, then you'll need to nail it to ground at intervals with additional small caps, with a much-sub-wavelength spacing.
At 12GHz, it will be very difficult to get your physical capacitor length down far enough to be a really good ground. It may be better to put series RCs between power and ground to sap energy from the resonance to tame it, rather than trying to kill it.
One of the main reasons for going to CPW is if the IC you're interfacing with has pins that suit it, like GND-sig-sig*-GND. This one doesn't, it's GND-sig-sig*-AVDD. It would be far less complicated to exit the IC differentially on sig-sig* and run differential microstrip. Or if you want to run CPW a long way from the device, via the AVDD to get it out of the way, and run your CPW between real grounds.
Don't forget that if your sig-sig* are balanced as they leave the IC, there are no signal currents flowing to ground anyway. If you want to introduce a ground, that's your choice for when you let the signals see some ground, rather than seeing their complements.