Chat on WAN

[blacksource]

chat on( sorry, my english is so poor that i don`t whether on or in ) WAN.
i have seen the programs from Matthew Millman and Yi Hai, but they all work on LAN only.
i found a article Peer-to-Peer (P2P) communication across middleboxes from google
quote from that article

Server S
18.181.0.31:1234
|
|
+----------------------+----------------------+
| |
NAT A NAT B
155.99.25.11:62000 138.76.29.7:31000
| |
| |
Client A Client B
10.0.0.1:1234 10.1.1.3:1234

Suppose A starts sending UDP messages to B's public address, however, and simultaneously relays a request through server S to B, asking B to start sending UDP messages to A's public address. A's outgoing messages directed to B's public address (138.76.29.7:31000) cause NAT A to open up a new communication session between A's private address and B's public address. At the same time, B's messages to A's public address (155.99.25.11:62000) cause NAT B to open up a new communication session between B's private address and A's public address. Once the new UDP sessions have been opened up in each direction, client A and B can communicate with each other directly without further burden on the "introduction" server S.

now, my question is that client A and client B send UDP messages to NAT B and NAT A without server S, whether the communication can be build.