Can you use cement board OVER an existing drywall for a new tile shower installation in a bathroom renovation?
Yes! This is actually a very common install method. I do drywall, plastic, then hardieboard on nearly half my tub shower surrounds. It is easier to work with 1/4" HB and I get flatter walls. You could make a point that this type of install is the most effective and long term in a lot of cases. For a stand-up shower I would however put something like redgard over the backer.
Is there a particular reason why you want to do this? Technically it shouldn't be a problem (as long as what you put over it is water-proofed correctly) but I wouldn't do it unless I had a clear reason to do so.
Also, the other comment I see mentions plastic under the Hardiebacker (which is perfectly fine) or Redguard over the Hardibacker (which is also fine) but, just to be clear, you don't want to do both. Two layers of water-proofing is not better than one (it just means that, if any moisture gets past the first layer, it is now essentially trapped).