Nope.
Gaz Emulator, along with SockMon, uses a subset of the TCP/IP protocol called UDP. UDP is a stateless, connectionless broadcast protocol. Way convenient, extremely fault tolerant, requires almost no overhead, but it is insecure, so Internet infrastructure & backbone routers have it trapped out. The cheap-o routers and switches most of us use (Linksys, D-Link, etc) have UDP pass-through enabled, but if you ever buy a really high-quality industrial-strength programmable switch or router (Cisco, for example), it will almost surely have UDP broadcasts disabled by default.
If you're ambitious, you can buy a pair of serial-to-TCP/IP protocol converters to accomplish what you're trying to do, but it'll be sticky and finicky due to Internet security issues. Both ends will have to have a static, routable IP address and either no firewall or a carefully configured firewall with forwarding set up correctly. I can give you the socket numbers TT*Ware uses if you want to try that.
Depending on the distance you're talking about, you'd be better off using directional, amplified "Pringle's Can" WiFi antennas to add the display site to your LAN. You can shoot those things up to around a mile, but they're not cheap and they have to be bolted to the side of a building & carefully aimed. One of my customers, The Australian Open, uses a rig like that to broadcast live tennis scores via WiFi across the main railroad tracks in downtown Melbourne from Rod Laver Arena to the player hotels. It's pretty cool. Obviously, if you're talking about broadcasting data from Telluride to Moscow, that's not an option.
Another option is contracting with a video shoutcast company to shoutcast a video image of Gaz Emulator over the internet. You can hook up a scan converter to your Gaz Emulator PC and feed it to them as live video. This type of service is getting pretty reasonable, price-wise, these days, and such companies have the mirroring & bandwidth infrastructure to handle the loads it pulls.