In case anyone was wondering about this, or perhaps if search engines pick this question up later.

The answer is yes. Apparently you absolutely can, specifically in this context which is probably not the one most people will be wishing for: With a SteamVR session driving a headset attached directly to that computer, you can indeed also initiate a Steam remote play/Steam Link session to stream that computer's VR preview window to a different computer for the purposes of viewing elsewhere, albeit apparently at a slightly reduced framerate. Even if both computers are not even running the same OS, and also evidently without setting the host computer on fire in the process. I'm as astonished as anyone else.

I did exactly this today using my Reverb G2 in my living room, which is normally connected to my fire-breathing gaming PC that's located in my office, a completely separate room, via the expedient of a stupidly long pair of DisplayPort and USB extension cables. Normally the preview is irrelevant as I am well versed in working completely within VR and using virtual desktops if I need to access flatland for anything. But I had a friend over who is not experienced with VR in the slightest and I wanted to have a view of what they were seeing in order to offer assistance while I could be there in the living room with them. I have a dinky media center PC connected to the TV in the living room. I settled on the above gimcrack solution rather than running yet another cable (which I certainly didn't have on hand anyway) and there you go.

Verily, it does not work if you try it the other way around. I had no expectation whatsoever that it would, but it was worth a shot. Apparently you can't initiate a remote play session of a VR game on your powerful computer if your headset is in fact plugged into a different computer. As a matter of fact, SteamVR won't even fully launch without a headset connected to the host PC. Also, my media center PC with its weedy several generations old budget Intel processor and integrated on-board graphics decelerator got very angry with me just for having the sheer effrontery to even plug my Reverb G2 into it.