The way the Index and its video output works is that it absolutely must be connected to the display via Displayport. The second you try to change it to HDMI or anything else, it will stop working. There is no way around this. I'm not sure the details but there is probably something specific about the way Index uses Displayport that an HDMI connection simply doesn't have the ability to handle/relay.

And so, since at the Vive Pro end the Index output will be inevitably connected via HDMI, it will just never be possible to connect the wireless adapter to the Index.

There's always a chance Valve could change something on the software end to make the Index's Displayport output able to be converted to HDMI in the future, but all signs have thus far pointed to this not happening or even being possible.