Computers while off to not just inhale dust. Yes the outside will collect some and some will make it into the system, but I do not think I would be too bad. It is a different story with top vents I guess.
I recommend you just cover it with a garbage bag(EDIT, beat to it) and switch off the power switch off the power supply(or power bar).
I am sure someone is going to say that will static kill the system with static shock, but the fact is static killing a system is 99% of the time from a human touching a part with them having the build up of static, not the other way around.
The other option is to place the system in its box that it's case shipped in if you still have it.