Y-Foil Frames Rear Suspension?
I can only speak based on what I have read, but my understanding is that A) yes it has a softer ride quality due to the lack of a seat tube, and B) it was banned for the lack of a seat tube. UCI is pretty strict on what they consider legal and what they don't.

In regard to your final question as it applies to road bikes, I would venture to say that the lack of a seat tube as it was designed for the frame in question does not provide any substantial advantages. Otherwise we would have seen more frames of this shape from other manufacturers and more of a push from the industry to legalize the design for UCI racing. There have been similar designs through the years such as the Softride. They also failed, because that frame shape just isn't an awesome design.