The really nice thing about plexiglass is that if you hit it with, like let's say, a flying drumstick or a toppling boom stand or an over zealous musician, it won't shatter into a mass of little glass pebbles. Plexi doesn't weigh a ton and is much easier to transport.
Sliding glass doors make a fairly good entryway into a moderately isolated drum room, but I don't know anyone that has used it as a drum sheild. I suppose it should work, but to me it sounds like a real pain and an accident waiting to happen.
Good luck with it.