You could in theory run an electric locomotive from a diesel generator in an adjacent vehicle, after all that is how slugs are run. But in order to get appreciable power and speed out of a gg1 you need a generator equivalent to a modern diesel electric. A GG1 is a 4000+ hp machine capable of using basically twice that in short bursts.
If you did rebuild a GG1 you are going to spend a huge amount of time trying to get it under the wire on the north east corridor so you might as well make it overhead wire and or third rail capable from the get go. I would think somebody will take this on as a challenge eventually. As I said earlier in theory this is somewhat simpler as the technology is still in everyday use. I do agree that it would probably be cheaper to build a replica than perform a restoration/revitalization of an existing model. Looking at various cross sections that GG1 was designed around style, so maintenance ability took a back seat. It looks like all the electrical components would need installed from overhead, where modern equipment can be serviced from a platform using a fork truck.
The traction motors are another concern. Each powered axle was driven by two motors through a quill drive. These would likely have to be retained and a single large traction motors per axle would require more room physically and a complete redesign of the power trucks.
When completed you would have a locomotive that could have current electronics in it, but still would be very cramped for the engineer and zero visibility out the other side of the cab, likely requiring a two man crew.
I say you still add flashing lights to the pantograph just for fun. And if you have the space and money you can still make provisions for "slug" style power from a generator car, although performance will be curtailed to the generator set ability.