With the new ShipStation integration, does Pressero alert ShipStation if a product in Pressero is marked to ship separately?

Yes.
 
In Pressero, we allow users to mark a product to ship separately. In this case, the product is considered to ship in its own box and the user is charged for that separate shipment.  This setting is found in Sites > [site name] > Catalog > Products > General tab in the CheckOut section.  
 
If a product is marked to ship separately, Pressero will send this item as a separate order in ShipStation.  For example, if a Pressero order contains three items - one marked to ship separately and two shipping to the same address and not marked to ship separately, Pressero would send two orders to ship station - the first order for the item marked to ship separately and the second order for the other two items that will be shipped in the same package.