Are you talking about borosilicate lab glass? Like an Erlenmeyer flask?
Borosilicate glass is pretty tough. I'd figure it would be tough to drill and melt together.
I'd like to know how it turns out though, man. That would be badass in the most dorky way possible.
Cut the bottom off a graduated cylinder and stick it into an Erlenmeyer with a test tube coming out the side for the mouthpiece... Sick!