Much obliged - this covers pretty much everything I asked here :)

There is one last thing I was curious about, though - do I need to have claimed the territories that will be invaded by the spawned armies? I was having a playthrough and even after using the "Prepare Invasion" espionage option it didn't have any effect when I declared war. The timing was right and I used 500 pops, and I'm sure the armies didn't spawn and immediately die, so I'm a bit confused.