Yes — but with one extra step. VR headsets use their own display pipeline, so the StreamVox teleprompter doesn't appear inside your headset automatically.
Why this happens
When a VR headset is active, Windows renders the VR scene through a separate display layer. Desktop overlay windows (StreamVox, Discord, OBS) live on the regular desktop layer — they're invisible to you while wearing the headset.
Fix: install a VR overlay companion app
You need a small companion app that pins desktop windows into the VR view. There are several free options.
Find a VR overlay app
Search Steam — or your headset's app store — for "VR overlay" or "desktop overlay". Several apps do exactly this; pick one with good reviews.
Point it at the StreamVox teleprompter
Open the overlay app, target the StreamVox teleprompter window, and pin it wherever you want in your VR scene.
After that the teleprompter floats in your VR space just like it does on your desktop. Translation keeps running through StreamVox on the host PC.