If I am understanding your question correctly you want to surround your room a vacuum so sound waves will not travel through your glass walls. In theory this would work very well but there are some major obstacles to overcome.
Say your room is quite small, $12$ by $12$ by $8$. From the standpoint of a vacuum, earths atmosphere is at $14.7$ psi. $12$ feet times $12$ feet equals $152$ tons of force on your ceiling and floor due to atmospheric pressure. ($12\ \text{ft}\times 12\ \text{ft} = 20726\ \text{in}^2$, $20726\ \text{"}^2 \times 14.7\ \text{lb/in}^2 = 304819\ \text{lb}$ or $152\ \text{tons}$)
Also at some point you are going to have to interface your inside box with your outside box for support and access. Any loud noises would vibrate the inside box which would vibrate your doorframe/supports, which would vibrate your outside box and the air as well. While the noise would probably be minimal it would not be 100% soundproof.
So to answer to your questions
- Theoretically yes but I doubt you have the time or money.
- No it would not be durable without very thick glass or some kind of internal and external support.
If you want to soundproof your room I would look into getting some foam padding specifically made to cancel sound waves. These will absorb sound waves and deter sound waves from traveling through your walls.
Here is a website that will help you get an idea of how to do what you want based on the reason you want to sound proof your room.