As a "Can it be done" question, the answer is definitely yes. G-Code is mostly movement instructions, after all.
In terms of automating the translation from G-Code to RAPID code, I've never personally seen how it is done.
Yes, you can use NX to program ABB robots to do any kind of machining. You have to have corresponing licenses!
When you setup а common CAM operation in NX for a common CNC machine, you don't have to specify machine type. But in robot case you have to create your robot's kinematic model and setup some additional robot rules. In short, that is a difference between CNC machine and a robot in NX.
NX generates a tool path listing (preliminary) in it's internal language.
NX post-processor geneates output file for your machine or robot from generated internal tool path listing.
NX have a basic ABB robot (RAPID) post-processor.
