No. The water leaking would then be expected to sit under shower based and on top of the moisture barrier? This might help diffuse an issue for a couple weeks but you would never know and might have a bigger issue.
What is your expectation here? If you put down lets say, a plastic sheeting, under backerboard... Well it will have screw holes everywhere and will leak. If you want your entire flooring waterproof like a big shower, then treat it like a shower and use something like a kerdi membrane or a paint on rubber membrane after your backerboard but before thinset. I have done both in bathrooms but most of the time neither. It depends on the importance of what is located below the bathroom. I personally install 1/2" durarock on bathroom floors. I lay out the backer so that the seams don't match the subfloor and also I try not to screw in the backer to the joists. If you had a 1" subfloor I could see going with 1/4" but this is hardly ever the case.
1) If it is labeled and approved as a "tile-ready" pan then you should not have to waterproof under it, there would probably be no effective way to do it anyway. Follow the directions that came with the pan and do what your local code enforcement authority says.
2) You may not even need to install cement board. If the floor is flat and sturdy plywood of sufficient thickness then you could lay the tile directly on the floor. Use a high quality thin-set mortar or tile adhesive that is specifically designed for bonding to wood. Read the label, it should be marked as "fortified" and should have language indicating max allowable deflection (flexing) of the substrate. No moisture barrier should be necessary, but don't leave standing water on the floor (obviously).