hah, ironic you mentioned that... as I built mine in the rain, it's actually sorta cool, because the leaves and amendments get sprinkled and evenly wet as you go..
BUT you need to tarp all compost piles, in my opinion. When finished, that is. Acts like a jacket for the thermo compost
Don't worry about wet leaves, they just start molding, and that's not a prob at all, my leaves were bagged for at least a week before using.
Gotta love that wet leaf smell.
but composting is just the stuff degrading, so bagged leaves aren't doing much different
you just accelerate it by the layering and such
--side note---
wet rained on shoes will attract your amendments if you have to stomp down your pile..
My boots got a nice crusty fish meal/shrimp meal on em...
mmmm yummy..