Two thoughts that come to mind. One, how can you get it out if you wanted to reuse the bottle. And two, if you can't get it out does the plastic prevent one from recycling the glass bottle?
I would not be reusing the bottles in the winery but I think you could easily pull them back out with a wire. I don't think there should be any problem for recycling. It would be such a small percent of the wight that it would be negligible. In the processing of the glass I'm sure all the labels and foils are the real issue to remove. It would come out in he wash so to speak.