Just an update... it works! But it's a bit wonky.
First, the controller has to be connected (via cable or bluetooth) to the TV's breakout box (which has USB ports), NOT to the PC.
Second, the TV's steamlink app just mirrors everything on the PC screen... and continues to control the PC as well. I'm not sure if this is the same behavior as the actual steamlink hardware. I assumed that the TV would run Steam, but the PC would still be useable (i.e. it would multitask) but the PC monitor mirrors the TV. Even after exiting out of steam, the connection is maintained, and you see the PC desktop on the TV. It's inelegant but does the job.
Finally, there are several potential conflicts between button mapping in steam, in launchbox, and in the emulator itself (I dislike retroarch, but I'm using it for simplicity at the moment).
The emulators seem fairly responsive, no major lag. This changes once you enter the GUI for the emulator; it gets heavy slowdown. It's not taxing the network or the PC, but I think it's just not optimized for my setup.
Running steam itself seems fine. The combination seems one layer of inception too deep. I had hoped to use my (brand new, powerful, home built) PC for emulation on the TV, but I will probably go back to my old atom-based Zotac and keep it to 16 bit and earlier, for now. I do wish there were an easy, elegant way to get bigbox on the TV, without steamlink and without lag.