Quite a few people have used lexan and plexiglass before, for things like magazine walls and other flat surfaces. It's pretty cool for magazines as you can see how many darts are inside. Outside of that, though, there isn't much advantage to using plexiglass as opposed to, say, PVC sheeting?
What exactly do you mean by making the "body, not innerds" out of plexiglass? I don't think anybody has ever bothered to make a seperate body and put internals inside like Nerf does.
I have to disagree with the Snazzy one, but I guess "easy" and "hard" to machine are all relative. My opinion however, is that plexiglass is quite easy to machine, though like he said, it can be a fairly brittle material. I've always just treated it like a brittle Aluminum: Deburr with a light file, tap it for any machine screws (though cyanoacrylate won't assist fracture!), but try not to put it under too much tension. It does crack easily, like the liquid tilt capacitor I made 5 months back.
Using solid chunks of polycarbonate is certainly a good way of prototyping, especially for visual display, but I don't know if all our members here really want to have to try and scrounge or buy chunks of it, or have the machining skill to make something that won't eventually crack and leak. Sure, we could all custom machine everything for our blasters out of aluminum, too, but then I fear it would be all too professional. I was always a big fan of the $5 hardware store solution for its ingenious simplicity.
That's a pretty cool BB gun.