No because to send data from machine A to machine B and get a response you endup with 2x the number of machine to backbone hops and that is where almost all the latency is. Try doing a traceroute to google.com, almost all the latency is between your house and the ISP.
Connections on the backbone are by comparison very fast.
Also in a 1v1 game you'd want to provide a consistent experience for both players and if one machine is acting as a "server" that player would have less latency and most likely an advantage.
Yap, it will be interesting to see how pricing change with dedicated server gaming as opposed to P2P gaming this gen. It will also be interesting to see how Sony react to dedicated server gaming this time.