I'm not sure exactly how it works, but I think flexing will take away from the performance of the speaker. Not to mention, when it flexes it will change the air space of the box, and probably rattle loose the silicone, or whatever you will use for a sealant. It might even vibrate. On top of that, you need it to insulate quite well so none of the inside sound escapes the box.
If I were you I would talk to a glass shop and try to get something thicker. But if you have it in there, why not try it out and see what it does.
Other than that the rest looks awesome. That is going to be a sweet looking enclosure. Very nicely done.
Murray