Sally,
Yes if large enough the pig is likely to pee/poo, esp if raining, as they get up walk away from bed, and then go to the loo.
But for an adult sow you would need a very large ark for this to happen - what size and type is it?
For people buying a few weaners, we recommend putting some straw bales (uncut) in to reduce size in the early days.
On floors, you are looking at both wet and cold, so ground temperature as well as whether the ground will get soggy needs to be considered. as you are planning to have litters using this ark, i would strongly recommend a floor - and as Markcott recommends 6*1 are good. It is easier to install in a competed ark. Plywood can easily become slippery, and you will not want mum slipping and falling on piglets.