This is very interesting. People who have had a laryngectomy can't speak post-operation, and being able to say something with their 'real' voice would be psychologically helpful.
Would it? Unless the sound is produced from inside their body in the same manner as natural, no it will sound weird just like playing back your own voice.
Not necessarily - people close to me were complaining about what they saw as losing a part of their identity ( and grandchildren definitely were not happy about the change).
Even for those who learn to speak with an oesophagal voice, being able to real time map it to something more natural would be great.
To be more specific, they consider themselves to be 'voice mutilated', even when able to speak, so I guess that anything closer to their original voice would be a net benefit.