No. I'm pretty sure. Not in the US or UK at least.
Looking up "glass gourd" on Google I find mostly gourd-shaped glass decorations and things that seem to be drawing from foreign languages (like argentinian maté cups, or something that looks suspiciously like what French would call "une gourde" that has nothing to do with the vegetable).
Which isn't to say it's completely impossible but I would say the only context where you'd say "I drank out of the glass gourd" and it would make sense is if you're talking with someone else who knows exactly what gourd-shaped glass bottle you're talking about and you're kind of winking at each other about it. Like if you had a cat-shaped bottle and said "I drank out of the cat": you'd both know what you mean but it's not a turn of phrase that's a general part of the language.
Basically "bottle" isn't a shape per se, it's a tool. Even if the tool is gourd-shaped, it's a bottle. If you don't call it a bottle then you're suggesting it's not that tool (for example it's decorative, or it's being used in an ad-hoc way for that tool's purpose but you're mostly focusing on its non-tool nature)