I may have had a very lucky day, but our show went on despite a pretty rainy day.
It poured off and on before our show, but was dry when we reported 30 min early. Well, the sky was dry, but they were busily toweling off the stage to get it dry. Either just before, or during our show, it started to rain a little again, and I put on my poncho. It turned out to be just that short spritz and our show went uninterrupted.
I am NOT trying to say my experience was typical - it sounds like you should be wary of potential closure, but I'd just suggest not giving up if it has been rainy or even raining lightly. If I had a big Star Wars fan (and had arrived at rope drop to sign up!) I would still show up and hope for the best.