Doran,
I don't know that I'd necessarily pull the prop, but, you want to keep the outdrive down, that makes sure all water is drained and nothing can collect in there, if it does, it can freeze and crack the case. If you think a flat tire would put the prop on the ground, pull it. It's good to pull the prop and grease the shaft (no jokes Gregg!) once a year anyway.
Anytime I pull a carb I shove t-shirts in the intake, if you think there are mice in the storage area that might chew through t-shirts, you could cut a template out of something to slide over the hole... Use the gasket as a pattern for the bolt holes on whatever you use for a "cover".