The glass on my stove is clean most of the time. We (the missus) probably cleans it once a month. There could be some fancy air wash feature that brings clean air down over the glass on its way to being burned.
Why not put glass in and see if it works? If it doesn't, it will turn black and just look like the rest of the stove. It's probably much easier to maintain a tiny firebox if you can see what's going on inside.
By the way, that's a beautiful little stove
