It would be nice if it could. If you could make antennas out of glass, you could have totally clear antennas or you could even turn an entire window into an antenna. That would be incredibly awesome.
Except, you can’t.
Glass is actually one of the least conductive things on the planet, despite being made partially of silicon, which forms the heart of nearly every computer chip, ever. That’s just how chemistry works, I guess. Computer chips are made from silicon and glass is made mostly of silicon dioxide and these are so different that one is a great conductor and one absolutely isn’t.
Glass is such a poor conductor of electricity that it’s used to insulate those massive power transformers and other big things the power company uses. Glass conducts heat and other forms of radiation very well, but it doesn’t conduct electricity for squat. The same is true of most ceramics, which are chemically similar to glass in the way they’re laid out.
Now, there is a bit of a back door here. Tinted glass is often made with bits of aluminum or other metal. If the glass is coated with a layer of aluminum oxide, which is a common way to tint it, that oxide layer would conduct electricity fairly well. So you could probably have a tinted glass antenna, although it’s not clear how well it would work (pun intended.) Most likely the relatively small amount of aluminum wouldn’t do a very good job of conducting. In order to test this you’d need to make a piece of tinted glass the exact shape of the elements in an antenna and test them side by side.
Note to self, head down to the tint shop and see if I can actually do this.
However, until I can get some real-world testing out there, I’m going to say no, you can’t have an antenna made of glass. If only we actually had transparent aluminum like we should have gotten by now.