It would also be physically impossible I'm pretty sure, to completely remove every single particle from an enclosed volume, as the more you remove, the harder it becomes to remove more? I dunno I'm not an experimentalist.
That's setting aside that even if you did somehow create a perfect vacuum in a box, you would then still have all the quantum fields permeating the box, some of which I guess would creat and annihilate virtual particles inside there continuously. A box that can block quantum fields would be truly impressive. Not sure what the hell you'd do with it but... it'd be a neat conversation starter :P
Aye, I mentioned them in my second paragraph :D
The actual reality of a virtual particle is a bit of an open question though from my (admittedly limited) understanding. They seem to just be a figment of the maths required to arrive at the on-shell processes. A guy I spoke to recently was rather dismissive about a particular area of research as they don't really bother with interactions that lead to external particles. Like "Oh we can calculate gg -> gggg scattering super-duper fast compared to the old methods!" "Great, how does that help us exactly?"