This isn't exactly the same as what you were describing... as you will still need to manually copy over the configuration file... BUT. As long as the "brewing PC" is running Windows XP Professional (or the right version of Vista but I don't know which versions support it), it has a Remote Desktop feature built-in.
I use this frequently from other PCs and from my MacBook (there's a Mac client available) to remote in to my main desktop.
Once you remote in, you control that computer as if you were sitting at it. So then, if you have a network drive mapped on your Brewing PC that connects to another computer on your network with your copy of BeerSmith on it, you can simply drag-n-drop the exported config file from the "server" to the Brewing PC. Then, you can open JBBS (still remotely), load the config file, and start the process running.
I've done this successfully over wireless, no ethernet cable required.
Cheers!