Yes, it is physically POSSIBLE to look through a drinking glass, but I would argue that this is not a good example to use as a sentence to teach language. Better to use the word for "glass" (what is that in Italian?) which one would commonly look through and not to confuse students. My humble opinion.
I don't think anyone would refer to a window in English by saying "the glass" so I don't know what the confusion is about. The window is made of glass (uncountable) whereas a glass or the glass is clearly a glass object made for the purpose of drinking, so a drinking glass.