The Marlins grounds crew is good (L*rd knows they get enough practice), but if they get this field anywhere near acceptable shape tonight, they've pulled off a miracle. Loria will owe them a huge tip - I hope they don't hold their breath.
I'm guessing the outfield will drain fairly quickly once the rain actually stops. The infield shouldn't be a huge issue assuming it didn't rain too much before they got the field covered and that there aren't any holes in the tarp...