As a recent convert to the benefits of tarps (thanks Roscoe for all your advice), I would put up a tarp ...
... but not my huge one.
I'd definately look at slinging a small one just to cover the tent, or even one of those lighter gazebo jobbies. Of course the fact that as soon as I pack up my camping gear I magically transform into my secret superhero status as The Rainmaker may be a factor.
If a man speaks in the middle of the forest and there is no woman around to hear him, is he still wrong?