Well, I think it would be a cool feature to people who live far away from each other and still wanna train together. Infinite Health would be nice, but being able to get a proper online Training with all features from the offline one would be best. I'll take what we get though... the game is shaping up quite nicely anyway.
Another cool feature that was in KoFXIII I think, was the ability to play Training mode while waiting for people to join your online room. It's probably a long shot, but that would be a very cool thing to have in DOA5 too.