CodeRush's approach to this kind of fix is more of an interactive process.
Which is to say you have to physically be in the location of the variable whose name you wish to change and you have to change each one individually.
That said, there is a very powerful engine under CodeRush called the DXCore, which can be used to create a very wide variety of functionality. Indeed it is this layer on which the whole of CodeRush and RefactoPro are built.
I have no doubt that it could be used to create the functionality you are after. However I doubt that you would use the existing rename technology. I will have to look into this a little further, but I am optimistic about being able to produce something.