Surprisingly low. Steam reports about 12-15ms latency over the 6GHz dongle, and the Internet seems to think that the capture card preview adds about 49 ms; I haven't tested the latter claim myself, but ~65ms feels like a reasonable number. I don't usually seem to notice <100ms latency when I play games (which could be a skill issue on my part), and indeed I don't notice delay between the VR headset image and the direct HDMI passthrough that goes to my desktop monitor (the non-dummy display)

I had initially only planned to use this setup for turn-based games, but after this pleasant surprise, it looks like I get to explore some other kinds of games :D