It does, at least in theory. It displays the option to enable VR for me on Chrome for Android which pops you into Google Cardboard. I can look around fine but without a controller I don't think there's a way to move.

For Chrome on Windows, I had to enable "WebXR Incubations" (chrome://flags/#webxr-incubations), manually start Steam VR, then restart Chrome. The option to enable VR appears, but then in the headset it's just a white screen. Maybe I'm missing a step or maybe it's just broken.