It has been purposefully painted to look like a glass cylinder; the white paint strategically placed to show it reflecting light coming from the left, and to give the appearance of glass. So I don’t think this represents an unfinished telescope. I would be skeptical that it is a telescope as I’m not aware of glass refractors, or why you’d want one. The end cap of the glass tube is different to the ends of the telescope near it on a mount.
We need an expert in glass artefacts of the C17th to indicate what a glass cylinder might have been used for. I was wondering what other material it could be; plastics weren’t known, rock crystal seems unlikely, ice again seems unlikely. So I would have thought it does represent glass.
Interesting story.