Problem is there that you are assuming both consciousness-es would operate identically, in perfect sync. In fact, from the moment the separated they would begin to diverge into different people on account of their separate experiences... Unless you decided to have a continuous open link operating on a massive level of emotional, sensory, and cognitive inter-connectivity.
Putting aside that it isn't clear if such a link is feasible with the human mind or EVE's technology, such a link would probably take even MORE bandwidth than just running a simple remote platform.
I will also add that I remember a comment from CCP somewhere on the EVE-O forums where they suggested top-of-the-line, bleeding-edge-compactness fluid router would be the size of a largish suitcase; most models would be closer to a large home refrigerator, so just slapping one onto a human-size platform isn't a possibility.