I will admit that when I did the (completely custom) intercooler setup on my '92, I also removed the A/C compressor, however that was mostly because I am extremely lazy, the A/C system had never worked in the first place, and I live in SoCal, where A/C is kind of pointless.
That said, I would posit that the vast majority of those Miatas which started out with A/C and then received a turbocharger kept their A/C system during the process. Both Bell and FM's turbo systems require no modification of the A/C system whatsoever to accommodate them.
What I'm saying, essentially, is that if you desire to keep the A/C functionality of the car, redesigning the system to accommodate an electrically-operated compressor seems like the extremely hard way of doing things as compared to simply routing the plumbing in such a way as to allow it to be retained as-is.
What manifold and turbo are you planning to use for this build?
On topic, what little I can find on the Prius' AC compressor indicates that it is driven by a 3-phase AC motor, powered from the main inverter and operating at (or near) the "nominal" battery voltage of 200-270 volts (varies by year.) I found one fellow who measured the power consumption of the device, and found it to draw around 1,700 watts, which is over 2HP- well outside of the range of practicality for a small DC motor, and nearly double the output of the stock alternator.
The closest thing I could imagine to a practical solution would be something like this: http://www.masterflux.com/products/sierra/
There are a couple of products on that page rated for use at 12v, with current/power loads that fall nearer to the range of "not insane" within the context of a Miata (220-450 watts). Remember, of course, that cooling performance as measured in btu/hr is going to drop as a function of power consumed, so you'll have to determine whether an A/C system with roughly one-third of the capacity of a Toyota Prius, installed in an old, leaky convertible with much more heat penetration into the passenger compartment from the drivetrain, is going to be adequate.